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GRE 9367 #18

Posted: Sat Sep 26, 2009 4:13 pm
by whateverNeveram3n
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! =)

Re: GRE 9367 #18

Posted: Sat Sep 26, 2009 8:28 pm
by Nameless
think abou the geometric series $$\frac{1}{1+x^{2}}=\sum_{n\geq 0}(-1)^{n}x^{2n}$$
now take the derivative both sides !

Re: GRE 9367 #18

Posted: Sun Sep 27, 2009 2:47 pm
by whateverNeveram3n
Aha--lesson learned to not psyche myself out before trying to manipulate a sum into a familiar form...

Thanks!