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(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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Give an example of a series with nonnegative terms where > a, diverges but > af 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 as > 0.
Transcribed Image Text:(a) Give an example of a series with nonnegative terms where > a, diverges but > af 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 as > 0.
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