## Alternating and Power Series Problems

1.) Let a0, a1, a2... be a nonincreasing sequence of positive numbers that converges to 0. Does the alternating series SUMMATION[(-1)^k]ak necessarily converge?

2.) Let r > 0 be arbitrary. Give an example of a power series SUMMATION(ak)x^k with radius of convergence r.

Any help would be appreciated.