2(In(n + 1) – In(n)). n=1 (a) Let a, = In(t 1) – In(n). Does the sequence {an}1 converge or diverge? (b) Let SN be the Nth partial sum of the series, that is %3D SN = (In(n + 1) – In(n)). n=1 Simplify this expression for SN as much as possible by rewriting the expression for SN without sigma notation (i.e. expand the sum). (c) Use your expression for SN from (b) to show that this series diverges. Could you have also concluded this from the Test for Divergence?
2(In(n + 1) – In(n)). n=1 (a) Let a, = In(t 1) – In(n). Does the sequence {an}1 converge or diverge? (b) Let SN be the Nth partial sum of the series, that is %3D SN = (In(n + 1) – In(n)). n=1 Simplify this expression for SN as much as possible by rewriting the expression for SN without sigma notation (i.e. expand the sum). (c) Use your expression for SN from (b) to show that this series diverges. Could you have also concluded this from the Test for Divergence?
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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Transcribed Image Text:(In(n + 1) – In(n)).
n=1
(a) Let an = In(h+1) - In(n). Does the sequence {an}1 converge or diverge?
%3D
=D1
(b) Let SN be the Nth partial sum of the series, that is
SN = (In(n + 1) – In(n)).
n=1
Simplify this expression for SN as much as possible by rewriting the expression
for SN without sigma notation (i.e. expand the sum).
(c) Use your expression for SN from (b) to show that this series diverges. Could you
have also concluded this from the Test for Divergence?
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