Alternating Series Theorem

Question

Use the Alternating Series Theorem to prove that the series which is the sum from n=0 to

infinity of a_n=(-1)ⁿ/n! converges

Answer 1

This is alterneting series.

Now test: 1. lim n→∞ (-1)ⁿ/n! = 0; 2. Ia_{n + 1}I = 1/(n +1)! < 1/n! = Ia_nI

Because given series converges