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Both of the following series converge by comparison to E= n=1 4n² 00 3 3 and 4n2 +7 2.4n? – 7 n=1 N=1 Explain and show why one series requires the Limit Comparison Test and the other one doesn't.

Both of the following series converge by comparison to E= n=1 4n² 00 3 3 and 4n2 +7 2.4n? – 7 n=1 N=1 Explain and show why one series requires the Limit Comparison Test and the other one doesn't.

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 Both of the following series converge by comparison to En=17n2 N=: 00 3 3 and 4n2 +7 4n2 – 7 N=1 N=1 Explain and show why one series requires the Limit Comparison Test and the other one doesn't.
Transcribed Image Text:3 Both of the following series converge by comparison to En=17n2 N=: 00 3 3 and 4n2 +7 4n2 – 7 N=1 N=1 Explain and show why one series requires the Limit Comparison Test and the other one doesn't.
Expert Solution
Step 1

Given two series are 

∑n=1∞34n2+7 and ∑n=1∞34n2-7

Step 2

Now,

∑n=1∞34n2+7<∑n=1∞34n2

So, Limit Comparison Test doesn't require to show the given series covergent.

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