Question

How do you find the power series representation for the function `f(x)=cos(2x)` ?

Answer 1

Since

`cosx=sum_{n=0}^infty (-1)^n{x^{2n}}/{(2n)!}`,

by replacing `x` by `2x`,

`f(x)=cos(2x)=sum_{n=0}^infty (-1)^n{(2x)^{2n}}/{(2n)!}`