Alternating series

• May 7th 2012, 04:25 PM
Bowlbase
Alternating series
summation:

$\sum\limits_{n=0} ^\infty \frac{(-1)^{n+1}n^n}{3^n^2}$

Using the root test and dropping the $(-1)^{n+1}$ I got:

$^n\sqrt{\frac{n^n}{3^n^2}}$

simplifies to:

$\frac{n}{3^n}$

To me it appears that any positive integer used will give the result of a ratio value of less than 1 and thus converges. However, wolfram tells me that it actually diverges. What am I doing wrong??
• May 7th 2012, 04:50 PM
skeeter
Re: Alternating series
how did you enter it in Wolfram?
• May 7th 2012, 05:32 PM
Bowlbase
Re: Alternating series
Dangit, I missed a carrot after the 3 in the denominator in wolfram. Now it works. I kept checking it but didn't notice the mistake until you asked that. Thanks a lot for the help