Find the Maclaurin series (i.e., Taylor series about c = 0) and its interval of convergence

Find the Maclaurin series (i.e., Taylor series about c = 0) and its interval of convergence

f(x) = cos2x

Use the fact that cos t = Σ(n = 0 to ∞) (-1)^n t^(2n)/(2n)!, convergent for all x.

Let t = 2x:
cos(2x) = Σ(n = 0 to ∞) (-1)^n 2^(2n) x^(2n)/(2n)!

Since t = 2x is a linear change of variable, this series also converges for all x.

I hope this helps!