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3. [Example 4.1.7 revisited] Let (bn)n≥1 be a sequence of real numbers such that lim bn = LE R. Define the sequence (an)n>1 by n-x an = bn -bn+1, n ≥ 1. n ak. (a) Simplify the nth partial sum Sn = Σ k=1 (b) Use (a) to prove that the (telescoping) series an is convergent. n>1 Find the sum of the series Σan. n=1 (c) Use (b) to prove that the series n>1 vergent and find the sum of the series. 1 n(n+1) m ((n ++1)n) is con-

3. [Example 4.1.7 revisited] Let (bn)n≥1 be a sequence of real numbers such that lim bn = LE R. Define the sequence (an)n>1 by n-x an = bn -bn+1, n ≥ 1. n ak. (a) Simplify the nth partial sum Sn = Σ k=1 (b) Use (a) to prove that the (telescoping) series an is convergent. n>1 Find the sum of the series Σan. n=1 (c) Use (b) to prove that the series n>1 vergent and find the sum of the series. 1 n(n+1) m ((n ++1)n) is con-

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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3. [Example 4.1.7 revisited] Let (bn)n>1 be a sequence of real numbers such that lim bn = LE R. Define the sequence (an)n>1 by 84x an = bn-bn+1, n ≥ 1. n (a) Simplify the nth partial sum Sn = Σ ak. k=1 (b) Use (a) to prove that the (telescoping) series an is convergent. n>1 Find the sum of the series Σ an. n=1 (c) Use (b) to prove that the series n>1 vergent and find the sum of the series. 1 n(n+1) In nn+1 (n+1) n is con-
Transcribed Image Text:3. [Example 4.1.7 revisited] Let (bn)n>1 be a sequence of real numbers such that lim bn = LE R. Define the sequence (an)n>1 by 84x an = bn-bn+1, n ≥ 1. n (a) Simplify the nth partial sum Sn = Σ ak. k=1 (b) Use (a) to prove that the (telescoping) series an is convergent. n>1 Find the sum of the series Σ an. n=1 (c) Use (b) to prove that the series n>1 vergent and find the sum of the series. 1 n(n+1) In nn+1 (n+1) n is con-
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