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following atemen may onsider usi Lay, Suppose that (an) is a bounded sequence and that the series converges absolutely. Then anbr converges absolutely.

following atemen may onsider usi Lay, Suppose that (an) is a bounded sequence and that the series converges absolutely. Then anbr converges absolutely.

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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Cauchy Criterion for Series states The infinate series ∑a_n converges iff for each ε > 0 there exists a natural number N such that, if n ≥ m ≥ N, then |am + am+1 + an| < ε.

(a) Prove the following statement. You may consider using the Cauchy Criterion (Lay, Theorem 8.1.6). Suppose that (an) is a bounded sequence and that the series converges absolutely. bn converges absolutely. Then anon
Transcribed Image Text:(a) Prove the following statement. You may consider using the Cauchy Criterion (Lay, Theorem 8.1.6). Suppose that (an) is a bounded sequence and that the series converges absolutely. bn converges absolutely. Then anon
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