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shutvik [7]
3 years ago
7

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

nvergence or divergence of the series using other methods.
[infinity] n = 1 n2/5n n = 1
lim n→[infinity] an + 1/an =
a. converges
b. diverges
Mathematics
1 answer:
jeka57 [31]3 years ago
5 0

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

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Mamont248 [21]

Solution:

f(3) = 3(x + 5 + 2)

f(3) = 3(3 + 5 + 2)

f(3) = 3(10)

f(3) = 30

Substitute 30 for a:

f(30 + 2)

f(32)

Best of Luck!

8 0
3 years ago
Lucy is going to walk in a fundraising event to raise money for her school band. Her mother has agreed to donate $7.50 to the sc
Readme [11.4K]

Answer: y = $7.50x + $25

Step-by-step explanation:

From the question, we are informed that Lucy is going to walk in a fundraising event to raise money for her school band and her mother has agreed to donate $7.50 to the school for each mile that Lucy walks, plus an additional $25.

The equation that represents y, the total amount of money Lucy's mother will donate if Lucy walks x miles during the event will be:

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Since Lucy walks x Mike's, we multiply x by $7.50 and then add the answer to the additional $25 which is the answer gotten above.

7 0
3 years ago
One side of a rectangle is 3 m more than the other. If the perimeter of the rectangle is 30 m, what are its dimensions? *
uranmaximum [27]

Answer:

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Step-by-step explanation:

you said One side— 3m MORE

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- You want to know the Perimeter. So we have to

add.

— so the expression is 3+3+x+x+x+x = 30

it is then simplified to 6+4x= 30

then we should be able to find out the X  which is 6

when we substitute the values with dimensions, you will get

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I hope This Helped!

6 0
3 years ago
If f(x)=1/9x-2 , what is f–1(x)?
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Lets get started :)

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This is the original equation, and now we have to find the inverse.

When finding the inverse, just flip the variables, x as y and y as x

f ⁻¹(x) 
  ↓
x = \frac{1}{9}y - 2
We have to isolate y as it is our f ⁻¹(x)

Take 2 to the other side { When you see subtraction, you do addition }
x + 2 = \frac{1}{9} y

Take 9 to the other side { When you see division, you do multiplication }
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7 0
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Answer:

(-3,0)

Step-by-step explanation:

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