In which of the following options, the statements given below and the generalterms an that satisfy these statements are matched correctly?I: >1is divergent when > an is convergentann=1n=1II: )is divergent when >anis divergentann=1n=1III: 2is convergent when the sequence {an}- is divergentann=11M: an =3n'K: an= n?L: an = Vn(а) 1-М(b) I-L(c)I-M(d)I-L(е) 1-КII - KП-МII - LII - KII - MIII - LIII -KIII - KIII- MIII - L

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Description: In which of the following options, the statements given below and the generalterms an that satisfy these statements are matched correctly?I: >1is divergent when > an is convergentann=1n=1II: )is divergent when >anis divergentann=1n=1III: 2is converg

We know that ∑1np is convergent for p>1 and divergent for p≤1 Consider K: an = n2{an} =…

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In which of the following options, the statements given below and the gener terms an that satisfy these statements are matched correctly? I: ) is divergent when an n=1 > an is convergent n=1 II: > is divergent when >an is divergent an n=1 n=1 III: E is convergent when the sequence {an}- is divergent an n=1 n=1 K: an = n² L: an = Vn M: an (а) 1-М (b) I-L (c) I-M (d) I-L (е) 1-К II - K II -M II - L II - K II - M III - L III -K III - K III- M III - L

In which of the following options, the statements given below and the gener terms an that satisfy these statements are matched correctly? I: ) is divergent when an n=1 > an is convergent n=1 II: > is divergent when >an is divergent an n=1 n=1 III: E is convergent when the sequence {an}- is divergent an n=1 n=1 K: an = n² L: an = Vn M: an (а) 1-М (b) I-L (c) I-M (d) I-L (е) 1-К II - K II -M II - L II - K II - M III - L III -K III - K III- M III - L

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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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

In which of the following options, the statements given below and the general
terms an that satisfy these statements are matched correctly?
I: >
1
is divergent when > an is convergent
an
n=1
n=1
II: )
is divergent when >an
is divergent
an
n=1
n=1
III: 2
is convergent when the sequence {an}- is divergent
an
n=1
1
M: an =
3
n'
K: an
= n?
L: an = Vn
(а) 1-М
(b) I-L
(c)
I-M
(d)
I-L
(е) 1-К
II - K
П-М
II - L
II - K
II - M
III - L
III -K
III - K
III- M
III - L

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