Thread: 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

thats a geo



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.

thank you!

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.