Mathematics: Test the series for convergence or divergence. ∑[infinity](n=1) (-1)^n/n5^n a. identify bn. b. evaluate the following limit. lim n → [infinity] bn

Test the series for convergence or divergence.

Ответ:

tubbs45

13.01.2022

The series converges, and the limit of bn when n→∞ is 0

Step-by-step explanation:

A) The nth term of this series is $b_n=\frac{(-1)^n}{n5^n}$ . We use the ratio test to decide the convergence of the series. Let $L=\lim_{n\rightarrow \infty}\frac{|b_n|}{|b_{n+1}|}$ . Then $L=\lim_{n\rightarrow \infty}\frac{n5^n}{(n+1)5^{n+1}}=\lim_{n\rightarrow \infty}\frac{1}{5}\frac{n}{n+1}=\frac{1}{5}$ . We obtain that

therefore the series converges.B) If we had $\lim_{n\rightarrow \infty} b_n \neq 0$ then by the divergent series test, the series $\sum b_n$ would be divergent which contradicts part A). We conclude that this limit must be 0.

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Ответ:

kekeke68

13.06.2021

Mathematics

So i calculated it is 20140 that
= 2.014*10 1
i believe i am corect like 90%
hope this helps

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Test the series for convergence or divergence.
∑[infinity](n=1) (-1)^n/n5^n
a. identify bn.
b. evaluate the following limit. lim n → [infinity] bn

Ответ:

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