By using the power series for f(x), find the power series for g(x) .

Question

By using the power series for  , find the power series for  .

Answer 1

If f(x) = 1 / (1-x), then f'(x) = 1 / (1-x)² and f"(x) = 2 / (1-x)³

The Maclaurin Series for 1 / (1-x) is ∑_{(n=0 to infinity)} xⁿ.

Differentiate twice to get the Maclaurin Series for 2 / (1-x)³.

I think that you'll get ∑_{(n=2 to infinity)} n(n-1)x^n-2.