Ratio test help -simple Question

Printable View

January 16th 2008, 09:37 PM
Joanna Jakma

Ratio 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!
January 16th 2008, 09:42 PM
Jhevon

Quote:

Originally Posted by Joanna Jakma

For the ratio test:

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

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!

do you mean $\frac {n^2}{(2n - 1)!}$ ?

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

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

by the way, what you wanted was 2(n + 1) - 1 = 2n + 1, not what you said before
January 16th 2008, 10:41 PM
Joanna 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 :(
January 16th 2008, 11:28 PM
mr fantastic

Quote:

Originally Posted by Joanna Jakma

CHeers for that!

Yes you got it right.
But surely
(2n-1)+1 = 2n? as opposed to 2n+1?

Yes, (2n-1)+1 = 2n. But that's NOT what Jhevon wrote at the end their post. Jhevon pointed out that

2(n + 1) - 1

is what you should have. And 2(n + 1) - 1 = 2n + 1.

2(n + 1) - 1 is NOT (2n-1)+1.