# Help with Power Series: Proof

• March 15th 2009, 07:46 PM
wyhwang7
Help with Power Series: Proof
Prove that for -1<x<1

1/(x+1) =

infinite
Σ [(-1)^n][x^n] = 1 - x + x^2 - x^3 + ...
n=0

ln(1+x) =

infinite
Σ [(x^n)(-1)^(n-1)]/n = x - (x^2)/2 + (x^3)/3 - (x^4)/4...
n=0
• March 15th 2009, 07:59 PM
matheagle
thats a geo

${1\over 1+x}={1\over 1-(-x)}=\sum_{n=0}^{\infty}(-x)^n$

Next integrate AND do not forget the +C, which by setting x=0 becomes 0.

AND your sum is wrong, you must start at n=1. You cannot divide by 0.
• March 16th 2009, 02:41 AM
wyhwang7
thank you!
• March 16th 2009, 06:27 AM
matheagle
Quote:

Originally Posted by wyhwang7
Prove that for -1<x<1
infinite
Σ [(x^n)(-1)^(n-1)]/n = x - (x^2)/2 + (x^3)/3 - (x^4)/4...
n=0

I hope your book does not start this sum at zero.
It looks like 1 to me.
You cannot divide by 0, anywhere.