# Math Help - find power series

1. ## find power series

find the power series representation of the function.

heres the equation: http://img260.imageshack.us/img260/9021/untitledph1.jpg

need help.
thanks.

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

heres the equation: http://img260.imageshack.us/img260/9021/untitledph1.jpg

need help.
thanks.
We know that, $-1
$\tan^{-1}x=x-\frac{x^3}{3}+\frac{x^5}{5}-...$
Know if you multiply this term by term for $(1+x^2)$ we have,
$x-\frac{x^3}{3}+\frac{x^5}{5}-....+x^3-\frac{x^5}{3}+\frac{x^7}{5}-...$
$x+\frac{2x^3}{3\cdot 1}-\frac{2x^5}{5\cdot 3}+\frac{2x^7}{7\cdot 5}-\frac{2x^9}{9\cdot 7}+...$

I just need to make the restriction,
$-1 rather then the endpoint because the Cauchy product applies only for the interval of absolute convergence.