3 1 -- + -- = 4 8 Pls answer quickly

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

jeka57 [31]

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.

5 0

3 years ago

What is the 5% of 300

garik1379 [7]

15
300*5/100 =15
That's all

5 0

3 years ago

Read 2 more answers

Free 5 points ig here you go have a great day and weekend and happy Valentin's day 1+5=6 yay somebody please get them im getting

lesantik [10]

Answer:

thenk you for the points give me brainlist pleasee

5 0

2 years ago

Read 2 more answers

a trader has 47,500 rupees with him. he placed an order for 22 items each costing rs. 1263. after making the payment for this pu

djverab [1.8K]

Answer:

since each item costs rs1263 we say

rs1263×22

27786

this means he spent rs27786

Her we now say rs47500-rs27786

=rs19714

This is to say that he has rs19714 left with him.

7 0

3 years ago

Read 2 more answers

Can someone solve this for me please.

nika2105 [10]

Answer:

The value of PR is 21 ft.

Step-by-step explanation:

We know that:

3(PQ + QT + TP) = PR + RS + SP
PQ = 7 ft.
QT = 4 ft
RS = 12 ft.

Work:

3(PQ + QT + TP) = PR + RS + SP
=> 3(7 + 4 + TP) = PR + 12 + SP
=> 21 + 12 + 3TP = PR + 12 + SP
=> 21 + 3TP = PR + SP
=> 21 + SP = PR + SP [3TP = SP]
=> 21 = PR

Hence, the value of PR is 21 ft.

Hoped this helped.

$BrainiacUser1357$

6 0

2 years ago

3 1 -- + -- =4 8Pls answer quickly