# Thread: power series representation

1. ## power series representation

find the power series representation.

heres the equation: http://img260.imageshack.us/img260/7458/untitledfl9.jpg

i'm horrible with integration. can someone provide me some steps please.
appreciate any help.

2. Originally Posted by rcmango
find the power series representation.

heres the equation: http://img260.imageshack.us/img260/7458/untitledfl9.jpg

i'm horrible with integration. can someone provide me some steps please.
appreciate any help.
The idea where is that function is not integratable.
$-\frac{ \ln (1-t)}{t}$.
But we know that, for $|t|<-1$
$\ln (1-t)=-t-\frac{t^2}{2}-\frac{t^3}{3}-...$
Let us make the resistriction $0.
Then,
$-\frac{\ln(1-t)}{t}=1+\frac{t}{2}+\frac{t^2}{3}+...$
Then if you integrate this,
$x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+...$