Answers
Answer:
[tex]\lim_{n \to \infty} U_n =0[/tex]
Given series is convergence by using Leibnitz's rule
Step-by-step explanation:
Step(i):-
Given series is an alternating series
∑[tex](-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
Let [tex]U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
By using Leibnitz's rule
[tex]U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }[/tex]
[tex]U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}[/tex]
Uₙ-Uₙ₋₁ <0
Step(ii):-
[tex]\lim_{n \to \infty} U_n = \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }[/tex]
[tex]= \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }[/tex]
= [tex]= \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }[/tex]
[tex]=\frac{1}{infinite }[/tex]
=0
[tex]\lim_{n \to \infty} U_n =0[/tex]
∴ Given series is converges
Related Questions
87 cities were surveyed to determine sports teams. 22 had baseball, 23 had football, 19 had basketball, 12 had baseball and football, 10 had baseball and basketball. 13 had football and basketball. 5 had all three. How many had only basketball?
Answers
Answer:
1 had only basketball hope that helps
Step-by-step explanation:
What percent of 25 is 50
Answers
Answer:
50 is 200% of 25
Step-by-step explanation:
50 is 200 percent of 25.
To find the percentage of one number in relation to another, we can use the following formula:
(Percentage / 100) * Base = Amount
In this case, we want to find what percentage of 25 is 50.
Let's use x to represent the percentage:
(x / 100) * 25 = 50
To solve for x, we can divide both sides of the equation by 25:
(x / 100) = 50 / 25
Simplifying:
(x / 100) = 2
Next, we can cross-multiply:
x = 100 * 2
Simplifying:
x = 200
Therefore, 50 is 200% of 25.
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30 points! Need help ASAP!
Answers
PLZ HELP BRAINLIEST
Create a scenario that requires use of the Fundamental Counting Principle to find the probability. Calculate the probability.
Answers
Answer:
see explanation below
Step-by-step explanation:
You have three pairs of shoes (white, brown, and black), and you have 6 pairs of pants ( brown, blue, grey, white, sand, and black)
We use the Fundamental Counting Principle to find the number of possible pant-shoe combinations:
3 * 6 = 18
then we can find the probability of wearing by random selection brown shoes with either blue or grey pants:
prob (brown shoes & blue pants) + prob (brown shoes & grey pants) =
= 1/18 + 1/18 = 2/18 = 1/9
The cost of hiring a taxi consists of a fixed cost of $3 plus $0.5 per kilometer distance travelled.
Write an expression in terms of y for hiring a taxi for y kilometers.
Answers
3 + 0.5y
Fifteen hungry kittens found a bucket of sausages. Each time they cut a sausage or a part of a sausage, they cut it into exactly two new pieces. They made 20 cuts in all and each kitten got 2 (maybe unequal) pieces of sausage. How many sausages were in the bucket?
Answers
Answer:
There is a total of 10 sausages. I am 100% sure.
Step-by-step explanation:
A bucket of sausages fed 15 hungry kittens. Each sausage or half of a sausage is sliced into two pieces. They chopped 20 sausages and gave each kitten two (perhaps unequal) portions. Therefore, there were 34,952 sausages in the bucket.
At the start, there is one sausage bucket, and the 15 kittens want to share it.
The first cut divides the sausage into two pieces.
After the second cut, there are four pieces of sausage.
After the third cut, there are eight pieces.
After the fourth cut, there are 16 pieces.
As we can observe, the number of pieces of sausage doubles with each cut. After 20 cuts, there will be 2²⁰ (2 raised to the power of 20) pieces of sausage.
Now, since each kitten received two pieces of sausage, the total number of sausages in the bucket can be calculated by dividing the total number of pieces by 2 × 15 (since there are 15 kittens).
Total sausages = (2²⁰) / (2 × 15)
Let's simplify this:
Total sausages = 2¹⁹ / 15
Now, let's calculate the value:
Total sausages = 524,288 / 15
Total sausages = 34,952.53
Since you can't have a fraction of a sausage, we need to round down to the nearest whole number.
Therefore, there were 34,952 sausages in the bucket.
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Phil bought two hamburgers and a milk shake
for $10.30. Janice bought three hamburgers and
a milk shake for $14.80. What is the cost of the
two milk shakes?
A. $1.30
B. $1.45
C. $2.60
D. $4.50
Answers
Answer:
C.
Step-by-step explanation:
[tex]\left \{ {{2x+y=10,3} \atop {3x+y=14,8}} \right.[/tex]
[tex]\left \{ {{y=10,3-2x} \atop {y=14,8-3x}} \right.[/tex]
10,3-2x=14,8-3x
x=4,5 - one hamburger
y=1,3 - one milk shake
OR:
$14,8-$10,3=$4,5 - one hamburger
2*4,5+y=10,3
y=1,3 - one milk shake
2y=2,6
You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that a prior survey suggests that about 22% of air passengers prefer an aisle seat. Assume that you want to be 98% confident that the sample percentage is within 5.1 percentage points of the true population percentage.
Answers
Answer:
358 randomly selected air passengers must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Assume that a prior survey suggests that about 22% of air passengers prefer an aisle seat.
This means that [tex]\pi = 0.22[/tex]
How many randomly selected air passengers must you survey?
We need a sample of n, and n is found for which [tex]M = 0.051[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.051 = 2.327\sqrt{\frac{0.22*0.78}{n}}[/tex]
[tex]0.051\sqrt{n} = 2.327\sqrt{0.22*0.78}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.22*0.78}}{0.051}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327\sqrt{0.22*0.78}}{0.051})^2[/tex]
[tex]n = 357.2[/tex]
Rounding up
358 randomly selected air passengers must be surveyed.
Click the picture
Giving brainlist
Answers
Answer:
5
The value of y is also 5!
The value of pair (x,y) is (5,5)
Hopefully this helped! :D
-LavenderVye
15 POINTS!!!IF YOU HELP ME!!!
1. A shopper bought a 10-pound bag of apples for $12.50. What was the unit price? Show your work. A $0.63 C $6.25 B $1.25 D $12.50
Answers
Which expressions are equivalent to 3 (62)?
Select each correct answer.
3(60 + 20)
3(6+2)
3(6+56)
03 (60+2)
Answers
Answer:
3(6 + 52)
Step-by-step explanation:
3(60 +20) = 3(80) ❌
3(6+2) = 3(8) ❌
3(6+56) = 2(62) ✅
A 16-foot ladder must reach 13 feet up a building. What's the measure of the angle
that the ladder makes with the ground?
OA) 39.090
OB) 3.6°
C) 54.34°
D) 35.66°
Answers
Do you wanna build a snowman or ride our bikes around the halls.
The correct answer is C) 54.34°.
Help!!
A class rolled number cubes. Their results are shown in the table.
What is the experimental probability of rolling a number less than 5?
67.8%
49.5%
34.4%
84.7%
Answers
Answer:
A. 67.8%
Step-by-step explanation:
the total number of occurences are 202
Now the total number of occurencess for 4 and below are 137
So Heres the quickest way to do it: Divide 137 by 202 then multiply it by 100 being 100%
Then you would get 67.8, then well put the percent sign behind it.
There are five boys to every nine girls in an introductory engineering course .if there are 364 students enrolled in the course , how many are boys ?
Answers
Answer:
234
Step-by-step explanation:
So what we know is that
5x+9x= students
This equation is saying that for every 5 boys there are 9 girls
we can then plug in 364 for the number of students and add like terms
This means that 14x=364
this means that x=26
This means that there are 26 sets of 5 boys and 9 girls
this means that there are
130 boys
234 girls
"Hunter read 40 pages in his history book in
one hour.
Rate of change is
Answers
The data distribution is ___
Answers
Skewed right
Explanation:
The data is higher on the right
Answer:
skewed left
Step-by-step explanation:
Simplify the rational expression by rationalizing the denominator √15/√6x
Answers
Answer:
√10/2x
Step-by-step explanation:
Multiply by √6 on the top and bottom to rationalize the denominator.
(√15×√6)/(√6x×√6) = √90/6x = (√9×√10)/6x = 3√10/6x = √10/2x
x^3 + 5x^2 + 2x + 10 = 0
Answers
Let's solve your equation step-by-step.
x3+5x2+2x+10=0
Step 1: Factor left side of equation.
(x+5)(x2+2)=0
Step 2: Set factors equal to 0.
x+5=0 or x2+2=0
x=−5
Answer:
x=−5
Help me please omg. Am having trouble with this.
Answers
Answer:
Part A 225-81=144
Step-by-step explanation:
1. 15×15 =225
2. 3×3×3×3 =81
What are the like terms in the expression 8 + x squared minus 4 x cubed + 5 x + 2 x squared?
8, 5 x
x squared, 2 x squared
8, 5 x 2 x squared
x squared, Negative 4 x cubed, 2 x squared
Answers
Answer:
B; x squared, 2x squared
Step-by-step explanation:
I took the test :))
Answer:
B; x squared, 2x squared
Step-by-step explanation:
hopefully this helped you
The train station clock runs too fast and gains 5 minutes every 3 days.
How many minutes and seconds will it have gained at the end of 7 days?
Answers
9514 1404 393
Answer:
mm:ss = 11:40
Step-by-step explanation:
We assume the amount of gain is proportional to the time that passes.
g/7 = 5/3
g = 7(5/3) = 35/3 = 11 2/3 . . . . minutes
The clock will have gained 11 minutes and 40 seconds after 7 days.
Esma and Hunter were trying to solve the equation:
x2 + 8x = 2x - 8
They both agreed they should first subtract 2x and add 8 to both sides and rewrite the equation as
22 + 6x + 8 = 0.
Then Esma said, "I can complete the square. I can add 1 to both sides to rewrite this equation as
22 + 6x + 9 = 1, factor, and solve using square roots."
Hunter said, "I'll factor the left-hand side of the equation as (x + 2)(x + 4) and solve using the zero
product property."
Whose solution strategy would work?
Answers
Answer:
Both
Step-by-step explanation:
Khan
Both of their strategies completing the square and factoring the left-hand side would work.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given a quadratic equation x² + 8x = 2x - 8.
They both agreed that first subtract 2x and add 8 to both sides and rewrite the equation as
x² + 6x + 8 = 0.
Both of their strategies would work.
As x² + 6x + 9 = 1
(x + 3)² = 1.
x + 3 = ± 1
x = ± 1 - 3.
x = - 2 or - 4.
x² + 6x + 8 = 0.
x² + 4x + 2x + 8 = 0.
x(x + 4) + 2(x + 4) = 0.
(x + 4)(x + 2) = 0.
x = - 4 or x = - 2.
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4 1/3 times 6
2 3/5 times 3 1/3
Answers
Answer:
8
8 2/3
Step-by-step explanation:
Put the following fractions in their simplest forms.
6/9
11/88
Answers
1/8
Would be the simplest forms
6/9 to 2/3
11/88 to 1/8
PLZ HELP ME WITH MY HW?????
Answers
Answer:
Uh 7/24?
Step-by-step explanation:
Just doing this in my head fyi lol
7 - 2x - 5y=-7
3x + 4y = 7
Answers
-5y = 2x
-5y/5 = y
2x/5 = 2x/5
y = 2x/5
4y = -3x + 7
4y/4 = y
-3x/4 + 7/4
y = -3x/4 + 7/4
10 POINTS
8TH GRADE MIDDLE SCHOOL MATH
Answers
Answer:
first one is the answer to this
Step-by-step explanation:
Pls help me with math ASAP
Answers
This means their angles add up to 180° which is a straight line
Answer:
Its c
Step-by-step explanation:
Howard buys a new comforter set for 15% off the original price of 54$.What is the sale price?
Answers
Answer:
$45.90
Step-by-step explanation:
What 15% off means is 85% of the original price ($54). 85% is the same as 17/20. Multiply 17/20 by 54 (or multiply 3/20 by 54 and subtract that from 54) to get the sale price.
(17 * 54)/20 (Multiply 17 by 54)
918/20 (Reduce if needed)
459/10 (Divide 459 by 10)
45.9
The sale price of the comforter is $45.90.
160% of 30
I’ve been stuck on this question for hours I REALLY need help
Answers
Answer:
The answer is 48
Step-by-step explanation:
160% is the same as 1.60
A percent of something means you have to multiply them together
1.60 times 30=48
Hope this helps!!
