In this question, we'll consider the series E (In(n + 1) In(n)). n=1 (a) Let...

 

Transcribed Image Text:

In this question, we'll consider the series E (In(n + 1) – In(n)). n=1 (a) Let an In(n + 1) – In(n). Does the sequence {a,}-1 converge or diverge? (b) Let SN be the Nth partial sum of the series, that is N 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 have also concluded this from the Test for Divergence? you In this question, we'll consider the series E (In(n + 1) – In(n)). n=1 (a) Let an In(n + 1) – In(n). Does the sequence {a,}-1 converge or diverge? (b) Let SN be the Nth partial sum of the series, that is N 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 have also concluded this from the Test for Divergence? you