**Problem Statement:**Prove that if \(\{x_n\}\) is a sequence such that \[|x_n| \leq \frac{1+n}{1+n^2}\]for all \(n \in \mathbb{N}\),then the sequence \(\{x_n\}\) is convergent and compute its limit.

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Answered: Prove that if {xn} is a sequence such…

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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Prove that if {xn} is a sequence such that 1+ n |æn| < for all n E N, 1+ n2 then the sequence {xn} is convergent and compute its limit.