## GRE 9367 #18

Forum for the GRE subject test in mathematics.
whateverNeveram3n
Posts: 3
Joined: Sat Aug 08, 2009 5:55 pm

### GRE 9367 #18

For problem #18, I can take the derivative of the sum ok, but then am stuck when it comes to actually figuring out what it converges to as n -> inf. Here's what I get for f':

$f'(x) = \sum_{n=0}^\infty (-1)^n (2n) x^{2n-1}$

Any help appreciated...thanks in advance! =)

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

### Re: GRE 9367 #18

think abou the geometric series $\frac{1}{1+x^{2}}=\sum_{n\geq 0}(-1)^{n}x^{2n}$
now take the derivative both sides !

whateverNeveram3n
Posts: 3
Joined: Sat Aug 08, 2009 5:55 pm

### Re: GRE 9367 #18

Aha--lesson learned to not psyche myself out before trying to manipulate a sum into a familiar form...

Thanks!