Question

power series representation by differentiation

Answer 1

you have formula for this problem, just apply
\[\dfrac{1}{(1-x)^2}=\sum_{k=0}^\infty (k+1)x^k\]
so that \[\dfrac{x^2}{(1-x)^2}=x^2\sum_{k=0}^\infty (k+1)x^k\]

Answer 2

uhm can i ask where did you get that formula? is it part taylor and maclaurin series?

Answer 3

thanks! :D