Originally Posted by

**Sprintz** Hello all; having some trouble with these last homework questions!

Instructions: Find a power series representation for the function and determine the radius of convergence.

#1) f[x] = x^2/(1-2x)^2

Should I use partial fractions to split this up?

As $\displaystyle \frac{1}{1-2x}=1+2x+4x^2+...+(2x)^n+...\,\,whenever\,\,|x|<\f rac{1}{2}\,,\,\,and\,\,since\,\,$ $\displaystyle \frac{2}{(1-2x)^2}=\left(\frac{1}{1-2x}\right)'\,,\,\,then...$

#2) Evaluate the indefinite integral as a power series. What is the radius of convergence. Integral of ArcTan(x^2)dx

$\displaystyle \arctan x=x-\frac{x^3}{3}+\frac{x^5}{5}-...\,,\,\,so \,\,\arctan x^2=x^2-\frac{x^6}{3}+...$

Tonio

Thanks so much for your help in the past and future all!