Question

Determine if the series abs converges, conditionally converges, or diverges.

n^n /n!

Answer 1

@terenzreignz

Answer 2

I don't know what test to use for convergence. For abs. conv. I used ratio test and well I got the limit as n approaches infinity of (n+-)^n / n^n

Answer 3

I'm not sure if its infinity or 1. There's a shortcut for when the limit approaches infinity, so that when the power on the top is the same as the bottom you take the coefficients. But is that just for polynomial functions?

Answer 4

Now you have \[\frac{(n+1)^{n}}{n^{n}}=\left( \frac{n+1}{n} \right)^{n}=\left( 1+\frac{1}{n} \right)^{n}\]
Oh that looks familar

Answer 5

e

Answer 6

Yup. So what conclusion do you reach about the series

Answer 7

Dang, I forgot about that :/ thanks! And it diverges

Answer 8

Yup. Sure thing

Answer 9

Do you have a suggestion on what test to use to see if it conditionally converges?

Answer 10

Its usually alternating series that do that, right. There is a test for that

Answer 11

I didn't think so since its not alternating sign. It's positive

Answer 12

Ah sorry. to see if a series converges conditionally see if the absolute value also converges. If it doesn't then you have conditional convergence

Answer 13

But don't you have to see if it converges without taking the absolute. Because they both can diverge

Answer 14

Yes. I mean after you confirm that the original series converges, check if the absolute does as well to check if its conditional

Answer 15

That's my problem, I don't know what test to use to see if original series converges

Answer 16

What is the series?

Answer 17

n^n /n!