What is the interval of convergence of \sum_{n=0}^{\infty} (cos x)^n?

1 Answer
Dec 31, 2017

See below.

Explanation:

Using the polynomial identity

(x^n-1)/(x-1) = 1+x+x^2+ cdots +x^(n-1)

we have for abs x < 1

lim_(n->oo) (x^n-1)/(x-1) = 1/(1-x)

then, for x ne k pi, k in ZZ we have

sum_(k=0)^oo (cos x)^k = 1/(1-cos x)