(a) Use differentiation to find power series representation for f(x)=1/(1+x)^2
What is the radius of convergence?
(b) Use part (a) to find a power series for f(x)=1/(1+x)^3
(c) Use part (b) to find a power series for f(x)=x^2/(1+x)^3
I found part (a) which was Σ n=0 to ∞ (1)^n(n+1)(x)^n, but I'm not sure how to use this for part (b). I thought something along the lines of:
1/(1+x)^3 = 1/(1+x)^2 * 1/(1+x)
and replace "1/(1+x)^2" with "Σ n=0 to ∞ (1)^n(n+1)(x)^n" Is this how I'm suppose to solve the problem?