Lesson 11-5 Alternating Series

Another Series Type Alternating Series – a series of numbers that alternate in sign, like the summation of the following infinite sequence ∑ is convergent if 1) b n+1 ≤ b n for all n 2) lim b n = 0 (note alternating part removed) (-1) n-1 b n n→∞

Types of Series Geometric Telescoping Harmonic P-Series Alternating

11-5 Example 1 (-1) n+1 series (alternating harmonic) n Alternating Series with b n+1 < b n Is the following series convergent or divergent? Lim b n = 0 so it might converge n→∞ so it will converge

11-5 Example 2 Is the following series convergent or divergent? Lim = 1/2 so alternate series test is N/A n→∞ 3n n - 1 so the series diverges by the Test for Divergence 3n (-1) n series n – 1 Lim = DNE n→∞ (-1) n 3n n - 1

Homework Pg 739: problems 3, 4, 7, 11