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2. Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a„}1 converge or diverge? (b) Let Sy be the Nth partial sum of the series, i.e. SN = (In(2n + 1) – In(2n – 1)) . n=1

2. Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a„}1 converge or diverge? (b) Let Sy be the Nth partial sum of the series, i.e. SN = (In(2n + 1) – In(2n – 1)) . n=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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2. Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,}1 converge or diverge? (b) Let Sy be the Nth partial sum of the series, i.e. SN =E (In(2n + 1) – In(2n – 1)). n=1 1. Simplify this expression for the Nth partial sum as much as possible by rewriting the 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 diverges. Could you have also concluded this from the Divergence Test?
Transcribed Image Text:2. Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,}1 converge or diverge? (b) Let Sy be the Nth partial sum of the series, i.e. SN =E (In(2n + 1) – In(2n – 1)). n=1 1. Simplify this expression for the Nth partial sum as much as possible by rewriting the 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 diverges. Could you have also concluded this from the Divergence Test?
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