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Let En 0 and (yn) be bounded. Prove nyn → 0.

Let En 0 and (yn) be bounded. Prove nyn → 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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Let \( x_n \to 0 \) and \((y_n)\) be bounded. Prove \( x_n y_n \to 0 \).
Transcribed Image Text:Let \( x_n \to 0 \) and \((y_n)\) be bounded. Prove \( x_n y_n \to 0 \).
Expert Solution
Step 1: Introduction

A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k, less than or equal to all the terms of sequence and another number, K', greater than or equal to all the terms of the sequence. Therefore, all the terms in the sequence are between k and K'.

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