# Help finding a power series

• Sep 29th 2008, 04:51 PM
paulrb
Help finding a power series
Using the power series of ln(1+x), find the power series of ln(x^2+1)

I found the power series of ln(1+x) which is,
x-(x^2/2)+(x^3/3)-(x^4/4)+...+[(-1)^(n+1)(x^n)]/n + ...

I don't know how to find the series for ln(x^2+1); the other problems involved using the anti-derivative or derivative of the original function but that doesn't seem to work here.
• Sep 29th 2008, 05:22 PM
skeeter
$f(x) = ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + ...$

so ... what is $f(x^2)$ ?
• Sep 29th 2008, 05:26 PM
paulrb
Ah thanks, that makes it easy. I just wasn't thinking from that perspective.