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Prove Tim Sn² = 5² if Um Sn=S

Prove Tim Sn² = 5² if Um Sn=S

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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Analysis. Please use the epsilon method.

**Problem Statement:** Prove that \(\lim (S_n)^2 = S^2\) if \(\lim S_n = S\). --- **Explanation:** This problem asks you to demonstrate a mathematical conclusion based on limits. Specifically, if a sequence \(S_n\) approaches a limit \(S\) as \(n\) approaches infinity, under what conditions does the square of the sequence \((S_n)^2\) approach \(S^2\)? This is a concept from calculus, where you explore the behavior of sequences and their limits, leveraging properties such as continuity of particular functions like squaring.
Transcribed Image Text:**Problem Statement:** Prove that \(\lim (S_n)^2 = S^2\) if \(\lim S_n = S\). --- **Explanation:** This problem asks you to demonstrate a mathematical conclusion based on limits. Specifically, if a sequence \(S_n\) approaches a limit \(S\) as \(n\) approaches infinity, under what conditions does the square of the sequence \((S_n)^2\) approach \(S^2\)? This is a concept from calculus, where you explore the behavior of sequences and their limits, leveraging properties such as continuity of particular functions like squaring.
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