- #1

SpicyPepper

- 20

- 0

## Homework Statement

Doing some problems from textbook, I need to determine whether the series is absolutely convergent, conditionally convergent, or divergent.

n!/n^n

I plugged it into WA, and it says the series doesn't converge, but I'm not sure how to figure it out.

## Homework Equations

## The Attempt at a Solution

First, I applied the root test

lim n->inf [tex]\frac{(n+1)!}{(n+1)^n} * \frac{n^n}{n!}[/tex]

lim n->inf [tex]\frac{(n+1)n!}{(n+1)(n+1)^n} * \frac{n^n}{n!}[/tex]

I reduce this, and apply the root test:

lim n->inf [tex]\sqrt[n]{\frac{n^n}{(n+1)^n}}[/tex]

lim n->inf [tex]\frac{n}{n+1}[/tex]

lim n->inf [tex]\frac{1}{1 + 1/n}[/tex]

= 1

1 means that it's inconclusive. I'm not sure if I applied the tests incorrectly or if I'm supposed to try something else.