Real Analysis II: Please adhere to sample example in 2nd photo to solve the problem!

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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Real Analysis II: Please adhere to sample example in 2nd photo to solve the problem!
2. Consider the series
1 1
+ + + + + +
3 5 3² 52 33 53 34 54
1x
(a) Show convergence or divergence by the Comparison Test.
(b) Show convergence or divergence by the Root Test.
(c) Why is there an issue to use the Ratio Test to show convergence
or divergence?
Transcribed Image Text:2. Consider the series 1 1 + + + + + + 3 5 3² 52 33 53 34 54 1x (a) Show convergence or divergence by the Comparison Test. (b) Show convergence or divergence by the Root Test. (c) Why is there an issue to use the Ratio Test to show convergence or divergence?
Com. ?
22. 1/21 + 1/32 + 1/23 + 1/34 + 1/25 + 1/36 + ½/27 + =
i j
aj+1
oold
= 3JH
j even →
Lim sup
Root test
j
j
دے
aiti
aj
Shp
Git!
aid = 400
aj
odd
even
2J+1
33
->
Root gives
=
نے
Z3J+1
aj
//
Q2mJ
Study linsuplajl's
= 1/25+1-34/₁
-1/2³+1 · 3/₁ = 31/3+1 = 1/2 - 3/0 -2 +00
包装.
Rafio Test is inconclusive (for conv.)
1/3-2/3 = 1/2 (7/3) 20
7
1/16
Linsup | 9j/4 = 1/2 = 1
Corw. of Series
\/as1's
½/2
1/3
Transcribed Image Text:Com. ? 22. 1/21 + 1/32 + 1/23 + 1/34 + 1/25 + 1/36 + ½/27 + = i j aj+1 oold = 3JH j even → Lim sup Root test j j دے aiti aj Shp Git! aid = 400 aj odd even 2J+1 33 -> Root gives = نے Z3J+1 aj // Q2mJ Study linsuplajl's = 1/25+1-34/₁ -1/2³+1 · 3/₁ = 31/3+1 = 1/2 - 3/0 -2 +00 包装. Rafio Test is inconclusive (for conv.) 1/3-2/3 = 1/2 (7/3) 20 7 1/16 Linsup | 9j/4 = 1/2 = 1 Corw. of Series \/as1's ½/2 1/3
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