power series representation

**rcmango** · February 8th 2007, 08:30 AM

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.

**ThePerfectHacker** · February 8th 2007, 09:34 AM

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 $0<t<1$ .
Then,
$-\frac{\ln(1-t)}{t}=1+\frac{t}{2}+\frac{t^2}{3}+...$
Then if you integrate this,
$x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+...$

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