Consider the sequence {an}1 where 1 1 an = 1++ The goal of this problem is to prove this sequence diverges to o. (a) Prove that for all k E Z with k > o 1 1 1 + + 2k + 2 1 + 2k 2k +1 2k+1 2 (b) Use (a) to prove that for all m E N a2m–1 >. (c) Deduce that {an}1 diverges to o.

Consider the sequence {an}1 where 1 1 an = 1++ The goal of this problem is to prove this sequence diverges to o. (a) Prove that for all k E Z with k > o 1 1 1 + + 2k + 2 1 + 2k 2k +1 2k+1 2 (b) Use (a) to prove that for all m E N a2m–1 >. (c) Deduce that {an}1 diverges to o.

Name: (1) Consider the sequence {an}1 where1an = 1+21+3+-...The goal of thi
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Description: (1) Consider the sequence {an}1 where1an = 1+21+3+-...The goal of this problem is to prove this sequence diverges to o.(a) Prove that for all k E Z with k > 0+ p11112k +12k + 22k+1(b) Use (a) to prove that for all m ENm25.a2m -1(c) Deduce that {an}-

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

(1) Consider the sequence {an}1 where
1
an = 1+
2
1
+
3
+
-
...
The goal of this problem is to prove this sequence diverges to o.
(a) Prove that for all k E Z with k > 0
+ p
1
1
1
1
2k +1
2k + 2
2k+1
(b) Use (a) to prove that for all m EN
m
25.
a2m -1
(c) Deduce that {an}-1 diverges to o.

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