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Finding the Sum of a Power Series 
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#1
Nov2706, 10:57 PM

P: n/a

I'm trying to find the sum of this:
[tex] \[ \sum\limits_{n = 0}^\infty {(  1)^n nx^n } \] [/tex] This is what I have so far: [tex] \[ \begin{array}{l} \frac{1}{{1  x}} = \sum\limits_{n = 0}^\infty {x^n } \\ \frac{1}{{(1  x)^2 }} = \sum\limits_{n = 0}^\infty {nx^{n  1} } = \sum\limits_{n = 1}^\infty {nx^{n  1} } \\ \frac{x}{{(1  x)^2 }} = \sum\limits_{n = 1}^\infty {nx^n } \\ \end{array} \] [/tex] So how do I get the (1)^n part in there? Any suggestions would be really helpful. Thanks. 


#2
Nov2706, 11:14 PM

P: 1,237

[tex] \frac{1}{1+x} = \sum_{n=0}^{\infty} (1)^{n}x^{n} [/tex]



#3
Nov2706, 11:28 PM

P: n/a

Oh, I see.. Where exactly does that come from?



#4
Nov2706, 11:29 PM

P: 1,237

Finding the Sum of a Power Series
[tex] \frac{1}{1+x} = \frac{1}{1(x)} = \sum_{n=0}^{\infty} (x)^{n} = (1)^{n}x^{n} [/tex]



#5
Nov2706, 11:44 PM

P: n/a

Ah! Of course. Okay. Thanks.



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