[tex] \displaystyle \sum_{n = 1}^{ \infty } {4}^{ - n} [/tex]
evaluation of the sum above ​

Answers

Answer 1

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

a is the first term in the seriesr is the common ratio

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

Learn more about Geometric Series here:

https://brainly.com/question/27737241

https://brainly.com/question/27948054


Related Questions


A hose fills a hot tub at a rate of 5.2 gallons per minute. How many minutes will it take to fill a 600 gallon hot tub? (nearest tenth)

Answers

Answer:

115.38 is what I got when I tryed to work it out

10 points need help finding area

Answers

Answer:

8 un^2

Step-by-step explanation:

to find this answer you must find the area of the rectangle and then the triangle

the rectangles area is

2 * 3 = 6 un^2

the traingle is

2 * 2 * 1/2 = 2 un^2

now you add them

6 + 2 = 8 un^2

Area is 8.:)))))))))))))


Find the smallest number such that
when divided by 18, the remainder
is 17, when divided by 20 the
remainder is 19 and when divided
by 24, the remainder is 23.

Answers

Answer:

I think the answer is 7

don't blame me if I'm wrong

Answer:

359

Step-by-step explanation:

the prime factors of the numbers are

18 = 2×3×3

20 = 2×2×5

24 = 2×2×2×3

the lowest common multiple is therefore

2×2×2×3×3×5 = 360

the difference between the checked divisor numbers and the expected remainder is constantly 1 :

18 - 17 = 1

20 - 19 = 1

24 - 23 = 1

so, we can deduct this constant 1 from the LCM and get the desired number :

360 - 1 = 359

verify :

359 ÷ 18 = 19 remainder 17

359 ÷ 20 = 17 remainder 19

359 ÷ 24 = 14 remainder 23

Which expression can be used to calculateof formalin needed make this batch of 3200 pd the amount? The batch sugar 3% water 39% formalin 44% melamine 14% total 100 amount of pounds equal 3200

Answers

The appropriate expression to identify the amount of formalin is: x = 3200 ÷ 100 × 44%

How to identify the amount of formalin?

To calculate the amount of formalin in this substance we must perform the following mathematical operation:

3200 ÷ 100 = 3232 × 44% = 1,408

According to the above, the mathematical expression would be:

X = 3200 ÷ 100 × 44%

Learn more about mathematical expression in: https://brainly.com/question/14462529

#SPJ1

find the roots of x^4-1=0​

Answers

Answer:

x = +1

x = -1

Step-by-step explanation:

x^4-1=0​

x^4=+1​

fourth root of x^4= fourth root of +1​

x = +1

x = -1

Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e

Answers

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

How to solve separable differential equation

In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.

[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]

[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]

[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]

[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]

If u = ㏑ y and du = dy/y, then:

[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]

[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]

[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]

[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]

[tex]C = (\ln e)^{3}[/tex]

[tex]C = 1[/tex]

And finally we get the explicit expression:

[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]

[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

To learn more on ordinary differential equations: https://brainly.com/question/14620493

#SPJ1

What is the present value of a cash inflow of 1250 four years from now if the required rate of
return is 8% (Rounded to 2 decimal places)?

Answers

Using simple interest, it is found that the present value of the cash inflow is of 947.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

In this problem, the parameters are given as follows:

r = 0.08, t = 4, A(t) = 1250.

We have to solve for A(0) to find the present value, hence:

A(t) = A(0)(1 + rt)

1250 = A(0)(1 + 0.08 x 4)

A(0) = 1250/1.32

A(0) = 947.

More can be learned about simple interest at https://brainly.com/question/25296782

#SPJ1

(h+k)(1) is
(k-h)(4) is
(k/h)(3) is
(h•k)(0) is
(k •h)(0) is
(h•k)(3) is
h(k(-2))

Answers

Answer:

Step-by-step explanation:

(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1

(k-h)(4)=k(4)-h(4)=0-(-1)=1

(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]

(h.k)(0)=h(0).k(0)=3(-2)=-6

(k.h)(0)=k(0).h(0)=-2(3)=-6

(h.k)(3)=h(3).k(3)=0(-1)=0

h(k(-2))=h(-3)=0

Need help anyone please!!!

Answers

the picture is blurred

A line has slope Four-thirds. Through which two points could this line pass?

Answers

Answer:

Two points this line can pass through (1, 4/3) and (2, 8/3)

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given:

slope = 4 / 3equation: y = 4/3x

we can plug in a number for x to find y

when x = 0,

y = 4/3(0)

y = 0

point: (0,0)

when x = 1,

y = 4/3(1)

y = 4/3

point: (1, 4/3)

when x = 2,

y = 4/3(2)

y = 8/3

point: (2, 8/3)

Learn more about slope and y-intercept here: brainly.com/question/12763756

Which of the following sets represents the range of the diagram below?​

Answers

The set that represents the range of the diagram below is given as follows:

B. {3, 5, 7}.

What is the range of a data-set?

It is the set that contains all possible output values.

In the diagram, we have that:

The input values are: {1,2,3,4,5}.The output values are: {3,5,7}.

Hence the set that represents the range of the diagram below is given as follows:

B. {3, 5, 7}.

More can be learned about the range of a data-set at https://brainly.com/question/24374080

#SPJ1

1. EL precio a la venta de una impresora de inyección de tinta es de $285.000 incluida una Ganancia del 35%. ¿cuánto le cuesta a la tienda cada impresora?

Answers

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

¿Cómo encontrar el precio de una impresora sin ganancia?

En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:

C' = C · (1 + r/100)     (1)

Donde:

C - Coste asumido por el vendedor, en unidades monetarias.C' - Coste para el consumidor, en unidades monetarias.r - Tasa de ganancia, en porcentaje.

Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:

285.000 = 1,35 · C'

C' ≈ 211.111,11

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

Para aprender más sobre ganancias: https://brainly.com/question/8421949

#SPJ1

Task
On April 15, 1912, the Titanic struck an iceberg and rapidly sank with
only 710 of her 2,204 passengers and crew surviving. Data on survival
of passengers are summarized in the table below. (Data source:
http://www.encyclopedia-titanica.org/titanic-statistics.html)
a.
First class passengers
Second class passengers
Third class passengers
Total passengers
Survived
201
118
181
500
Did not survive
123
166
528
817
Total
324
284
709
1317
a. Calculate the following probabilities round your answers to three decimal points
i. If one of the passengers is randomly selected what is the probability that this passenger survived
iii. If one of the passengers is randomly selected what is the probability that this passenger was in first class and survived
iv. If one of the passengers is randomly selected from the first class passengers what is the probability that this passenger survived
v. If one of the passengers who survived is randomly selected what is the probability that this passenger was in first class
vi. If one of the passengers who survived is randomly selected what is the probability that this passenger was in third class?

Answers

The probability that a random passenger survived is 0.38

The probability that this passenger was in first class and survived is 0.153

The probability that the passenger in the first class survived is 0.620

The probability that the passenger that survived was in first class is 0.402

The probability that the passenger that survived was in third class is 0.362

What are the probabilities ?

The probability that a random passenger survived is 500 / 1317 = 0.38

The probability that this passenger was in first class and survived is 201 / 1317 = 0.153

The probability that the passenger in the first class survived is:  201 /324 = 0.620

The probability that the passenger that survived was in first class: 201/500 = 0.402

The probability that the passenger that survived was in third class is: 181 / 500 = 0.362

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1

Analyze the conditional statement below and complete the instructions that follow.
If an angle measures 90°, then it is a right angle.
Identify ~q.
O An angle does not have measure 90°.
OIt is not a right angle.
An angle measures 90°.
OIt is a right angle.

Answers

Answer: It is not a right angle.

The movement of the progress bar may be uneven because questions can be worth more or less (including zera
Round 608 to the nearest hundred.
O 610
Type here to search
O 700
O 500
O 600
4
Oi
1

Answers

Answer:

600

Step-by-step explanation:

Because the tens digit is less than 5, round down to 600

answer: 610 because you started at 608 and u need to get the nearest 10

Determine whether it is a function

Answers

Answer:

Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.

What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216

A.220
B.240
C.864
D.1,296

Answers

Answer: D

Step-by-step explanation:  

6^4 = 6 x 6 x 6 x 6 = 1,296

6^4 = 1,296

Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .

If l is parallel to p what is the equation of l ?

Answers

The slope of line p is -5, so substitute into point-slope form, we get

[tex]\boxed{y-37=-5(x+2)}[/tex]

Which of the numbers below are whole numbers?
A. 6282
B. 650
C. 87
D. 99.8
E. 442.49
F. 1/10

Answers

Answer:  A B C

Step-by-step explanation:

A whole number is like 1,500 and a nonwhole number is like 33.2 or like 55/100.  

And have a good day.

A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32.
a. Compute the value of the test statistic

Answers

The value of the z test statistic will be 2.55.

What is the z test statistic?

The z test statistic is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z test statistics is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A sample of 25 provided a sample mean μ = 14 and a sample standard deviation σ = 4.32.

Then the value of the z test statistic will be

z = (x – μ) / σ

z = (25 - 14) / 4.32

z = 11 / 4.32

z = 2.546 ≈ 2.55

More about the z test statistic link is given below.

https://brainly.com/question/15016913

#SPJ1

A baby weighed only 8.7 ounces at birth. How much lighter was she than an average baby, who weighs about 7 lb 8 ounces?

Answers

The baby is 111.3 ounces or 6.96 pounds lighter than an average baby.

What is weight ?

Weight is the measurement of Gravitational force on an object.

It can be zero as in the space.

It is given in the question that

A baby weighed only 8.7 ounces at birth

weight of an average baby is 7lb 8 ounces

1 lb = 16 ounce

an average baby weight = 7 * 16 +8 = 120 ounces

The baby weight is just 8.7 ounces

so the baby is 120-8.7 = 111.3 ounces lighter than an average baby.

To know more about weight

https://brainly.com/question/10069252

#SPJ1

Help please I need asap

Answers

Answer: -120

Step-by-step explanation:

[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]

what is π x 5
please tell me the answer as quick

Answers

Pi: 22/7
Pi x 5 = 22/7 x 5

15.71428571428571

Identifying Proportional Relationships


Which graph represents a proportional relationship?

Answers

Answer:

I can't answer this if you don't have the answer choices

I'm sorry

Which statement is true about the end behavior of the graphed function?

Answers

Step-by-step explanation:

both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.

For a population with μ = 60 , X=81, and σ = 12. Find the z-score for 81.

Answers

The z-score for 81 is 1.75

How to determine the z-score for 81?

The given parameters are:

μ = 60 , X=81, and σ = 12

The z scores is calculated using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

Substitute the given values

[tex]z = \frac{81 - 60}{12}[/tex]

Evaluate the difference

[tex]z = \frac{21}{12}[/tex]

Simplify

z = 1.75

Hence, the z-score for 81 is 1.75

Read more about z-scores at:

https://brainly.com/question/25638875

#SPJ1

write an exponential expression that shows (10 to the power of 4) to the power of 4 simplified

Answers

Answer: it could be

[tex](10^{4} ) ^{4}[/tex]

Step-by-step explanation:

What is the length of BC¯¯¯¯¯?

Answers

Answer:

meight you gotta do better then that

Step-by-step explanation:

a picture is probably necessary

The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 2 5 10 32

Answers

The multiplicative rate of change of the function f(x) = 2 × 5ˣ is 5.

What is Exponential Function?

An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bˣ, where b > 0 and b ≠ 1.

The function is given as:

f(x) = 2 X 5ˣ

The above function is an exponential function.

An exponential function is represented as:

f(x) = abˣ

Where b represents the multiplicative rate

By comparison;

b = 5

Thus, the multiplicative rate of change of the function is 5.

Learn more about exponential functions from:

brainly.com/question/11464095

#SPJ1

Answer:

B!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

y = 5x+1150Use your functions to calculate the total cost for each fridge after 6 months.

New Fridge:

Answers

Answer:

[tex]x = \frac{y - 1150}{5} [/tex]

Step-by-step explanation:

[tex]y - 1150 = 5x \\ \frac{y - 1150}{5} = x \\ x = \frac{y - 1150}{5} [/tex]

Other Questions
When calculating turnover of property plant & equipment and receivables, which item from the income statement do we use? Operating expenses, Sales, Gross profit, Net income Give an example where the state intervened in the practices of religious community which violated the freedom and the fundamental rights of the people What is the main reason why Sotomayor refers to the saying a wise old man and wise old woman will reach the same conclusion in deciding cases? HELP!!!!!The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?g(x) = 3x-6g(x) = 3x+6g(x)=3*-6g(x)=3*+6 What embyonic germ layer gives rise to liver? write in slope intercept form2y+x=1 Oxygan is an example of a(n) 5 causes of examination malpractice Find one-third of the sum 9 and 12. 2 divided by what times what equals 7 What event is depicted in the photographs in Part One?Why are the photographs historically significant? The line y = 2x intersects the line y = x + 6 at the point A. Find the equation of the line that passes through A and has gradient 3 HELP PLEASE IT IS URGENT!!Why does the PPF bow outward?a) Because, while costs of sacrificedproduction may remain constant, thereare diminishing returns as moreresources that are freed-up may beless productive in the secondindustry.b) Because as more of one good isproduced, costs of sacrificedproduction may increase as resourcesbetter suited to production of thesacrificed good are freed-up toproduce the other product.c) Neither of the above.d) Both of the above. Select the correct answer.What is the tone of the passage telling all Americans stories: introduction to indigenous heritage?O A.bitterO B.celebratoryO c.frustratedO D.humorous how do i solve this?? You are mailing invitations to new medicare beneficiaries for a marketing event. You want an idea of how many people to expect, so you would like to request rsvps. What should you keep in mind?. What measurements should you use for large amounts of energy transfer Following are the number of automobile accidents that occurred at 60 major intersections in a certain city during the fourth of July weekend: 0 2 5 0 0 5 0 1 3 1 1 0 2 4 3 0 1 2 0 3 0 1 21 6 5 3 0 a) Group these data into a frequency distribution showing how often each of the values occur and draw a bar chart. 4 4 5 2 1 0 4 3 4 0 4 0 1 6 2 1 2 NN 2 4 5 230 2 1 1 4 2 2 4 0 1 0 b) Convert the distribution obtained in (a) above into a cumulative "or more "distribution and draw its ogive. Following are the number of automobile accidents that occurred at 60 major intersections in a certain city during the fourth of July weekend : 0 2 5 0 0 5 0 1 3 1 1 0 2 4 3 0 1 2 0 3 0 1 21 6 5 3 0 a ) Group these data into a frequency distribution showing how often each of the values occur and draw a bar chart . 4 4 5 2 1 0 4 3 4 0 4 0 1 6 2 1 2 NN 2 4 5 230 2 1 1 4 2 2 4 0 1 0 b ) Convert the distribution obtained in ( a ) above into a cumulative " or more " distribution and draw its ogive . Which of these is a reason that geographic isolation causes speciation?A. It decreases the chance that two or more populations of the samespecies will diverge.B. It makes the males and females of the affected populations moreattractive.C. It increases the chance that populations of the same species willinterbreed.D. It prevents gene flow between different populations of the samespecies. Read this excerpt from Susan B. Anthony's "Is it a Crime for a Citizen of the United States to Vote? " and complete the sentences that follow.But is urged, the use of the masculine pronouns he, his and him, in all the constitutions and laws, is proof that only men were meant to be included in their provisions. If you insist on this version of the letter of the law, we shall insist that you be consistent, and accept the other horn of the dilemma, which would compel you to exempt women from taxation for the support of the government, and from penalties for the violation of laws. . . .So long as any classes of men were denied their right to vote, the government made a show of consistency, by exempting them from taxation. When a property qualification of $250 was required of black men in New York, they were not compelled to pay taxes, so long as they were content to report themselves worth less than that sum; but the moment the black man died, and his property fell to his widow or daughter, the black woman's name would be put on the assessor's list, and she be compelled to pay taxes on the same property exempted to her husband. The same is true of ministers in New York. So long as the minister lives, he is exempted from taxation on $1,500 of property, but the moment the breath goes out of his body, his widow's name will go down on the assessor's list, and she will have to pay taxes on the $1,500. So much for the special legislation in favor of women.Susan B. Anthony makes two compelling arguments to suggest that women should be given the right to vote. She attacks the argument of the anti-suffragists that . She argues that since , all women should be afforded the right to vote.