What is >>>>> -x<15-2x

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

Evaluate 66 - 20 - 32 1/4

BigorU [14]

Answer:

13.75

Step-by-step explanation:

66-20- 32 1/4

66-20- 32.25

46-32.25

13.75

8 0

3 years ago

If two triangles have three corresponding angles and three corresponding sides that are equal in measure, are the two triangles

nikitadnepr [17]

Yes, they are.

If the triangles have three corresponding angles equal means that they are either similar or congruent.

The definition of congruent means that the sides have the same length. That is precisely what the statement says.

So, being the lengths of the corresponding angles the same the two triangles are identical, this is they are congruent.

6 0

3 years ago

Read 2 more answers

HELPPP PLEASE WILL NAME BRAINLIEST

laila [671]

The first reaction represented is a decomposition reaction due to the fact the bonded pair are being split apart.

The second equation is a single displacement because the B and C have switched places, which is the only change making it a single displacement. If there had been another bond and A had also moved, it would be double.

7 0

3 years ago

Read 2 more answers

PLEASEEE HELP I WILL MARK YOU BRAINIEST!!!

lisabon 2012 [21]

Answer:

26

Step-by-step explanation:

duh....

7 0

3 years ago