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

Printable View

- Mar 15th 2009, 07:46 PMwyhwang7Help 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 - Mar 15th 2009, 07:59 PMmatheagle
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. - Mar 16th 2009, 02:41 AMwyhwang7
thank you!

- Mar 16th 2009, 06:27 AMmatheagle