Consider the series >(In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,} converge or diverge? (b) Let SN be the Nth partial sum of the series, i.e. N SN =E (In(2n +1) - In(2n – 1)). n=1 Simplify this expression for the Nth partial sum as much as possible by rewritin expression for SN without sigma notation (i.e. expand the sum). (c) Use your expression for the Nth partial sum from (b) to show that this series dive Could vou have glso conchuded this from the Divergence Test?
Consider the series >(In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,} converge or diverge? (b) Let SN be the Nth partial sum of the series, i.e. N SN =E (In(2n +1) - In(2n – 1)). n=1 Simplify this expression for the Nth partial sum as much as possible by rewritin expression for SN without sigma notation (i.e. expand the sum). (c) Use your expression for the Nth partial sum from (b) to show that this series dive Could vou have glso conchuded this from the Divergence Test?
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:Consider the series
> (In(2n + 1) In(2n – 1)).
n=1
(a) Let a, = In(2n +1) – In(2n – 1). Does {a,} converge or diverge?
(b) Let Sy be the Nth partial sum of the series, i.e.
Sy = (In(2n +1) – In(2n – 1))
n=1
Simplify this expression for the Nth partial sum as much as possible by rewriting the
expression for Sy without sigma notation (i.e. expand the sum).
(c) Use your expression for the Nth partial sum from (b) to show that this series diverges.
Could you have also concluded this from the Divergence Test?
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