How to Determine Whether a Series Converges or Diverges Using an Alternating Series Test | Calculus | Study.com

SOLVED: Theorem 2.7.7 (Alternating Series Test). Let (an) be a sequence satisfying a1 >= a2 >= a3 >= ... >= 0. Then, the alternating series Σ((-1)^n * an) converges.Proof: The conditions of this theorem are outlined in Exercise 2.7.1. One consequence of these conditions is that an >= 0 for all n. Several proofs of Definition 2.7.8 - Convergence of a Series are given in Exercise 2.7.1.Exercises Exercise 2.7.1. Proving the Alternating Series Test (Theorem 2.7.7) amounts to showing that the sequen