xnlghtmarexgo
2021-11-23
Answered

Find whether the series diverges and its sum:

$\sum _{n=1}^{\mathrm{\infty}}{(-1)}^{n+1}\frac{3}{{5}^{n}}$

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Florence Pittman

Answered 2021-11-24
Author has **15** answers

Notice that

Since

and the sum converges because

pseudoenergy34

Answered 2021-11-25
Author has **22** answers

I also need the answer for this question

asked 2021-01-31

Use the Limit Comparison Test to prove convergence or divergence of the infinite series.

$\sum _{n=2}^{\mathrm{\infty}}\frac{n}{\sqrt{{n}^{3}+1}}$

asked 2022-01-21

Find the value of $\sum _{r=1}^{4}\frac{1}{2-{a}^{r}}$ where ${a}^{k}(k=0,1,2,3,4,5)$ are fifth roots of unity.

asked 2022-01-21

How to evaluate the sum:

$S}_{n}=\sum _{k=1}^{n}\frac{k}{{k}^{4}+\frac{1}{4}$

asked 2022-03-02

A bit rusty on this stuff. The whole problem is proving this is true:

$2\le 1+\sum _{m=1}^{n}\frac{1}{m!}\le 1+\sum _{m=1}^{n}\frac{1}{{2}^{m-1}}<3$

asked 2020-12-21

Determine the convergence or divergence of the series.

$\sum _{n=1}^{\mathrm{\infty}}\mathrm{ln}(\frac{n+1}{n})$

asked 2022-01-21

What options do I have for this series? No idea how to do it.

$\sum _{k=1}^{\mathrm{\infty}}\frac{{\mathrm{cos}}^{2}\left(k\right)}{4{k}^{2}-1}$

asked 2021-01-15

It is important to distinguish between

$\sum _{n=1}^{\mathrm{\infty}}{n}^{b}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\sum _{n=1}^{\mathrm{\infty}}{b}^{n}$

What name is given to the first series? To the second? For what values of b does the first series converge? For what values of b does the second series converge?

What name is given to the first series? To the second? For what values of b does the first series converge? For what values of b does the second series converge?