# ratio test problem

• May 8th 2007, 05:59 PM
jeph
ratio test problem
sum n=1 oo n^n / (n)!

a_n+1 / a_n =

edit: looked funny when i typed it in...
(n+1)^(n+1) / (n+1)! times n! / n^n

=

[n^n(n+1)^n(n+1)] / n+1 = n^n(n+1)^n

did i do the algebra right? what do i do next? ><
• May 8th 2007, 06:44 PM
ThePerfectHacker
Quote:

Originally Posted by jeph
sum n=1 oo n^n / (n)!

Ratio test.

(n+1)^(n+1)/(n+1)! * n!/n^n

(n+1)^(n+1)/[(n+1)*n!] * n!/n^n

(n+1)^n/n^n

[(n+1)/n]^n

[1+1/n]^n

The limit is e>1

Thus it does not converge.
• May 8th 2007, 08:29 PM
jeph
Quote:

Originally Posted by ThePerfectHacker
Ratio test.
[(n+1)/n]^n

[1+1/n]^n

The limit is e>1

Thus it does not converge.

how did you turn the first n to a 1 in the first part?

how did you get e? i dont get it...
• May 9th 2007, 03:42 AM
ThePerfectHacker
Quote:

Originally Posted by jeph
how did you turn the first n to a 1 in the first part?

how did you get e? i dont get it...

(n+1)/n = (n/n)+(1/n)=1+1/n

Now the limit you need to memorize is that,

(1+1/n)^n ---> e