representation of functions as power series

a) use differentiation to find a power series representation for f(x)= 1/(1+x)^2

what is the radius of convergence?

my answer: sigma from n =1 to infinity of (-1)^n[nx^(n-1)] R = 1 is this right. should n start at one or zero.

b) use part (a) to find a power series for f(x)= 1/(1+x)^3

my answer:n =1 to infinity of (-1)^n[n(n-1)x^(n-2)] is this right too R =1

c) use part (b) to find a power series for f(x)= x^2/(1+x)^3

my answer: n =1 to infinity of (-1)^n[n(n-1)x^(n)] is this right too R =1

is this right too?