(a) Give an example of a series with nonnegative terms where > ak diverges but E a% converges. k=1 k=1 (b) Prove that if ) ak converges and each ak > 0 then > af converges. k=1 k=1 (c) Show by example that (b) does not hold if we do not require that ak > 0.
(a) Give an example of a series with nonnegative terms where > ak diverges but E a% converges. k=1 k=1 (b) Prove that if ) ak converges and each ak > 0 then > af converges. k=1 k=1 (c) Show by example that (b) does not hold if we do not require that ak > 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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