Problem : What is the radius of convergence of x n ? of (- 1)n x n ?Since the radius of convergence only has to do with absolute convergence, the answer to the two parts will be the same. Since x n is a geometric series, it converges whenever x≤1 , but does not converge when x = 1 . Therefore, r = 1 is its radius of convergence.
Problem : Using the fact that
|e x = 1 + x + + + ... + + ...|
|e = 1 + 1 + + + ... + + ...|