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.
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.
$\displaystyle -\frac{ \ln (1-t)}{t} $.
But we know that, for $\displaystyle |t|<-1$
$\displaystyle \ln (1-t)=-t-\frac{t^2}{2}-\frac{t^3}{3}-...$
Let us make the resistriction $\displaystyle 0<t<1$.
Then,
$\displaystyle -\frac{\ln(1-t)}{t}=1+\frac{t}{2}+\frac{t^2}{3}+...$
Then if you integrate this,
$\displaystyle x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+...$