Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is arn interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)

[infinity]

Σ (-1)n+1(x-8)/n8n

n=1

Answers

Answer 1

I'm guessing the power series given is

[tex]\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-8)^n}{8^n}[/tex]

which you can condense somewhat into

[tex]\displaystyle -\sum_{n=1}^\infty \left(\frac{8-x}8\right)^n[/tex]

You should recognize this as a geometric series, which converges for

[tex]\left|\dfrac{8-x}8\right|<1 \implies |8-x|<8 \implies \boxed{0 < x < 16}[/tex]


Related Questions

NO LINKS!!


On the grid below, which point is located in the quadrant where the x- and y-coordinates are both negative numbers?

Answers

Answer:

Point c

Step-by-step explanation:

A is at (6,4), both +

B is at (-4,2) only 1 -

C is at (-7,-2) both -

D is at (5,-4) only 1 -

Hope that helps

Answer:

C

Step-by-step explanation:

C is the answer because dude just look at it. C is in the quadrant where both x and y axis is negative.

Hope This Helps You:)

Any polygon with two pairs of parallel opposite sides is a parallelogram

Answers

Answer:

It is false that any polygon with two pairs of parallel opposite sides is a parallelogram. Let's understand the answer in detail. Explanation: ... There can be other polygons that have more than 4 sides but have only two pairs of parallel sides, which can't be called a parallelogram.

Step-by-step explanation:false.

N/2-11<-7 solve the 2 step inequality

Answers

Answer:

N<6

Step-by-step explanation:

Add 11 to both sides then multiply by 2

2,826 rounded to the nearest tenth

Answers

Answer:

2,830

Step-by-step explanation:

Jenny's great grandmother is 95 years old.
Jenny is 12 years old.
What percent of Jenny's great grandmother's age is Jenny's age?

Hurry! Worth a lot of points!

Answers

Think of it as 12/95. 12.63

I need help answering asap!

Answers

Answer:

4 is. R=11.94 D= 23.88

5 and 6 I am not sure tbh

7 D=60.50 R=30.25

8 D=60 C=120

please urgent i beg for help !!!!!!!!!!!!!!!!!!!! will mark brainlist

Answers

Step 2 is incorrect. Since we are flipping the numerator and denominator, the exponents sign should be the opposite! In this case, it would become -5x.

Hope this helps!

is it Substitution or linear combination?​

Answers

Answer:

Substitution

Step-by-step explanation:

You would solve this system using the substitution method as one of the variables are define.

In other words y = x + 3 defines y with the expression "x + 3" and we are easily able to substitute this into the other equation for y and solve of x.

Suppose $\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$. What is the smallest possible value for $x$?

Answers

The smallest possible value of x is the value less than 2/3

Given the series [tex]$\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$[/tex]

We need to find the smallest possible value of x as shown:

[tex]\frac{1}{x} > 1\frac{1}{2}\\ \frac{1}{x} > \frac{3}{2}\\[/tex]

Reciprocate both sides

[tex]x < \frac{2}{3}[/tex]

Hence the smallest possible value of x is the value less than 2/3

Learn more on inequality here: https://brainly.com/question/4192645

Answer:x=7

Step-by-step explanation:

What is the smallest two-digit integer $n$ such that switching its digits and then adding 3 results in $2n$

Answers

We can write

n = 10a + b

where a and b belong to {1, 2, 3, …, 9}.

Swapping the digits produces a new number

n' = 10b + a

and adding 3 to this number makes up 2n,

n' + 3 = 2n

or

(10b + a) + 3 = 2 (10a + b)

so that

19a - 8b = 3

Since we want n to be the smallest possible 2-digit number that meets the criteria, let's start with a = 1. Then solving for b, we find

19 - 8b = 3

16 = 8b

b = 2

So, the number we're looking for is n = 12.

Just to confirm, swapping the digits gives 21, and 21 + 3 = 24 = 2•12.

orignal price on a comb 0.99 discount 55%

Answers

Answer:

I think 5.45?  Sorry, not the best at math

Step-by-step explanation:

if you get a 55% discount off of 0.99 cents you pay 0.45 $

you're saving 0.54 $

what does relatively prime mean in math?

Answers

Answer:

When two numbers have no common factors other than 1.

Step-by-step explanation:

In other words there is no value that you could divide them both by exactly (without any remainder).

21 and 22 are relatively prime:

• The factors of 21 are 1, 3, 7 and 21

• The factors of 22 are 1, 2, 11 and 22

(the only common factor is 1)

But 21 and 24 are NOT relatively prime:

• The factors of 21 are 1, 3, 7 and 21

• The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

(the common factors are 1 AND 3)

Relatively Prime is also called "coprime" or "mutually prime".

Here we see that 12 and 16 are NOT relatively prime

2. Given < MCP = 65°, find the measurement of arc MP , arc MRP and < MRP.​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

We know that the Angle subtended by an arc on centre of the circle is double as that of Angle subtended by the same arc on the circumference (boundary) of the circle

So,

[tex] \sf \angle MCP = 2\angle MRP[/tex]

[tex] \sf65 \degree = 2 \angle MRP[/tex]

[tex] \sf\angle MRP = 65 \degree \div 2[/tex]

[tex] \sf\angle MRP = 32.5 \degree[/tex]

Answer:

arc MP = 65°arc MRP = 295°angle MRP = 32.5°

Step-by-step explanation:

The measure of an arc is the same as the measure of the central angle it subtends.

  arc MP = ∠MCP = 65°

Long arc MRP is the difference between arc MP and the full circle:

  arc MRP = 360° -65° = 295°

Inscribed angle MRP is half the measure of the arc it subtends:

  ∠MRP = (arc MP)/2 = 65°/2 = 32.5°


Find the product
(-2) (7)

Answers

Answer:

-14

Step-by-step explanation:

Remember that a negative times a positive is negative:

(-2)(7) = -(2)(7) = -14

-14; because + and a negative equal a negative

What is the median of the following data values?
10, 11, 12, 15, 19, 24, 27, 29, 33, 38

Answers

Answer:

21.5

Step-by-step explanation:

Make sure they are in order.

A median is basically (or literally) the number in the middle of the data set.

In this case, it is 19 and 24. To get the middle number, you have to:

Add the two numbers and divide them by 2.

19 + 24 = 43

43/2 = 21.5

Identify all of the congruent corresponding parts. Then, write a congruence statement.

Answers

Angle C is congruent to angle S. Angle B is congruent to angle R. Angle A is congruent to angle D. Line AB is congruent to angle DR. Angle BC is congruent to angle SR. Angle AC is congruent to angle DS. There is nothing congruent in the single triangles but the triangles are congruent to each other.

PLEASE HELP.
A group of bacteria has a population of 100,000. The growth rate is 20%. How much bacteria will there be in 10 years? Use the exponential formula.

Answers

Answer:

200,000 i don't know apologies if it's wrong

Step-by-step explanation:

100,000*.20*10

200,000*10

200,000

can someone pllsss help :((
What is the area?

7 square feet
11 square feet
9 square feet

Answers

Answer:

7 square feet

Step-by-step explanation:

There are seven squares, one is 1 square foot

7x1=7

Shapes. I will give brainless answer correctly and tell me the number

Answers

Answer:

It has to be 4 parts because it will to uneven if you cut diagonally.

1. Bob makes $14 per
hour, plus $50 a day for
working. Write an
expression to represent
how much money Bob
makes in a day.

Answers

Answer:

$14(h) + $50 = t

t = total

h = hours he works



Please help me
A?
B?
C?
D?

Answers

Answer:

B

Step-by-step explanation:

Answer:

[tex]13x^{10}[/tex]

Step-by-step explanation:

[tex]4x^{10}+9x^{10}[/tex]

[tex](4+9)x^{10}[/tex]

[tex]13x^{10}[/tex]

Because [tex]x^{10}[/tex] can be factored out from both terms, you just add 9 and 4 and keep the [tex]x^{10}[/tex].

A rhombus has a side length of 6 centimeters, and a height of 2
centimeters.
What is the area of the rhombus, in centimeters??

Answers

Answer:

12 cm^2

Step-by-step explanation:

The area of the rhombus is 12 cm².

Given that, a rhombus has a side length of 6 centimetres, and a height of 2 centimetres.

We need to find the area of the rhombus, in centimetres.

What is the area of the rhombus?

The formula for the area of the rhombus when base and height are known.

The rhombus is a parallelogram. We know that the area of a parallelogram is given by multiplying base and height sq units. The same is applied to the rhombus as well. Area of a rhombus = Base × Height sq units.

Now, the area of a rhombus= 6×2=12 cm²

Therefore, the area of the rhombus is 12 cm².

To learn more about the area of the rhombus visit:

https://brainly.com/question/15458057.

#SPJ2

Please help me with this

Answers

Answer:

8 3/42, 34 1/2, 11 1/49 3/4, 16 1/4Y/B = 2/3

Step-by-step explanation:

a)

The first line is simply the sum of the two given numbers.

  3 1/2 +5 1/4 = (3+5) +(2/4+1/4) = 8 3/4

__

To find values on the remaining lines, it is convenient to find the ratios of the numbers involved. The ratio of yellow to blue is ...

  Y/B = (3 1/2)/(5 1/4) = (7/2)/(21/4) = (7/2)(4/21) = 2/3

Then ...

  Y : B : total = 2 : 3 : 5

This tells you the numbers on the second line are ...

  Y = 2; B = 3

__

The value for B on the third line is the basic ratio number multiplied by (6 3/4)/3 = 2 1/4. Then the other two numbers are ...

  Y = 2(2 1/4) = 4 1/2

  total = 5(2 1/4) = 11 1/4

__

The value for Y on the fourth line is the basic ratio number multiplied by (6 1/2)/2 = 3 1/4. Then the other two numbers are ...

  B = 3(3 1/4) = 9 3/4

  total = 5(3 1/4) = 16 1/4

_____

b)

The equation is the one we used to find the values on the second line:

  Y/B = 2/3

Can someone help me

Answers

Answer:

i) 0.1056

ii) 0.105

iii) 0.1

iv) 0.1056

Step-by-step explanation:

0.36, to the power of 2 (0.36×0.36) is 0.1296

0.1296-0.03×0.8=0.1056

Write an expression for 5 times the difference of twice a number and 4

Answers

Answer:

1. 50-x

2. 2x+189

3. x+109

4. x+99

5. x*(76-39)

6. 75+x

7. 45-3x

8. 2x+15

9. 3x-25

10. x*(x+88)

Step-by-step explanation:

y-3=? Help please!! Thank you!

Answers

Answer:

\mathrm{Axis\:interception\:points\:of}\:Y-3:\quad \mathrm{X\:Intercepts}:\:\left(3,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-3\right)

Step-by-step explanation:

It's just y-3 because they aren't like terms if you're talking about algebra.

This question was brief so I'm not sure what you're a skin but this is the algebra answer.

3x+1
can you solve it

Answers

Answer:

donwload the gautmaht this is very powerful calculator

Someone help me with this for BRAINLIEST thank you!

Answers

Hope it helps.

Don't forget to click the Brainliest button if you like my answer and if you have any query, please feel free to ask in the comment section.

[tex]x+y =6 ~~~.....(i)\\\\x =3y -2~~.....(ii)\\\\\text{Substitute}~ x =3y-2~ \text{in equation (i):}\\\\\\3y -2 +y =6\\\\\implies 4y = 6+2\\\\\implies 4y = 8\\\\\\\implies y =\dfrac 84 =2\\\\\text{Substitute y =2 in equation (ii):}\\\\x = 3(2) -2\\\\\implies x = 6-2 =4\\\\\\\text{Hence,}~ (x,y) = \left(4, 2\right)[/tex]

Help me with this problem please.

Answers

The value of x is 5. The value of y is 8.66.

The image attached is that of a right triangle. In order to determine the value of x and y, SOHCAHTOA would be used.  x is he opposite side and y in the adjacent side to the angle 30 degrees.

Sin 30 = opposite / hypotenuse

0.5 = x / 10

x = 5

Cos 30  = adjacent / hypotenuse

0.8660 = y / 10

y = 8.66

A similar question was answered here: https://brainly.com/question/18055768

No files or links please!

graph y= -4/3 x+2 using the slope and y-intercept


slope: 3


y-intercept: (0,-2)

Answers

this is the line as it passes through (-2) and 3
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