- #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.