Analysis explainwhether it is convergent, divergent to t∞, or otherwise divergent (not to±∞). If it is convergent, find its limit. If it is divergent, find its lim sup andlim inf.Sn=(-1) 2√n + 122n - 3Sn = n = n²

explain whether it is convergent, divergent to ±∞, or otherwise divergent (not to too). If it is convergent, find its limit. If it is divergent, find its lim sup and Tim inf. Sn S. = (−1)n-2√n + 12 2n - 3 = n - n 2

explain whether it is convergent, divergent to ±∞, or otherwise divergent (not to too). If it is convergent, find its limit. If it is divergent, find its lim sup and Tim inf. Sn S. = (−1)n-2√n + 12 2n - 3 = n - n 2

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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Question

Analysis

explain
whether it is convergent, divergent to t∞, or otherwise divergent (not to
±∞). If it is convergent, find its limit. If it is divergent, find its lim sup and
lim inf.
Sn
=
(-1) 2√n + 12
2n - 3
Sn = n = n²

Expert Solution

Step 1

What is Sequence:

When a sequence approaches a finite number as the variable approaches infinity, that finite number is referred to as the limit of a sequence. For a convergent sequence, the limit superior and limit inferior are equal to the limit of the sequence. Therefore, when these two limits are different, one can infer that the sequence is not convergent.

Given:

Given sequences are:

$s_{n} = \frac{{(- 1)}^{n} 2 \sqrt{n} + 12}{2 n - 3}$

$s_{n} = n - n^{2}$

To Determine:

We test the convergence of the sequences.

Step by step

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