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**mturner07** Hey guys, I have some infinite series problems I need my solutions checked to.

**Problem 1.** Use the ratio test to determine whether the series converges or diverges. Explain how the test permits you to draw your conclusion.

$\displaystyle \Sigma^{\infty}_{n = 1}\frac{n^n}{n!}$

__My Solution__

$\displaystyle \lim_{n \to \infty}\frac{n^{n + 1}}{(n+1)n!}*\frac{n!}{n^n} = \lim_{n \to \infty}\frac{n}{n + 1} = 1$

Since $\displaystyle \lim_{n \to \infty}\frac{\frac{n^{n + 1}}{(n + 1)!}}{\frac{n^n}{n!}} = 1$, the ratio test fails.

Here, I have trouble thinking my solution is right because the directions make no mention of the test failing. Is my solution correct?

**For problems 2 and 3 determine whether the series converges absolutely, converges conditionally, or diverges. Explain how you drew your conclusion in each case.**

**Problem 2.**

$\displaystyle \Sigma^{\infty}_{n = 1}(-1)^{n}\frac{e^n}{n!}$

**Problem 3.**

$\displaystyle \Sigma^{\infty}_{n = 1}(-1)^{n}\frac{1}{\sqrt{2n + 1}}$

I don't know how to do either of these problems, help please!

Thanks in advance for all help!