For the ratio test:

Is (2n-1) + 1 = 2n?

I have to use the ratio test to evaluate n2/(2n-1)! where n=1 for an infinite series...exam in a few hrs!

Printable View

- Jan 16th 2008, 09:37 PMJoanna JakmaRatio test help -simple Question
For the ratio test:

Is (2n-1) + 1 = 2n?

I have to use the ratio test to evaluate n2/(2n-1)! where n=1 for an infinite series...exam in a few hrs! - Jan 16th 2008, 09:42 PMJhevon
yes...this should be simple algebra for someone dealing with series. and what does this have to do with the ratio test?

Quote:

I have to use the ratio test to evaluate n2/(2n-1)! where n=1 for an infinite series...exam in a few hrs!

if so, we want to see if $\displaystyle \lim \left| \frac {\frac {(n + 1)^2}{(2n + 1)!}}{\frac {n^2}{(2n - 1)!}} \right| = \lim \left| \frac {(n + 1)^2}{n^2} \cdot \frac {(2n - 1)!}{(2n + 1)!} \right|< 1$

if so, the series $\displaystyle \sum \frac {n^2}{(2n - 1)!}$ converges absolutely

by the way, what you wanted was 2(n + 1) - 1 = 2n + 1, not what you said before - Jan 16th 2008, 10:41 PMJoanna Jakma
CHeers for that!

Yes you got it right.

But surely

(2n-1)+1 = 2n? as opposed to 2n+1?

So when doing the ratio test should it not be 2n! as opposed to (2n+1)! in that equation? I'm confused :( - Jan 16th 2008, 11:28 PMmr fantastic