n=1 ) Let a, = In(2n +1) – In(2n – 1). Does {an}1 converge or diverge? ) Let SN be the Nth partial sum of the series, i.e. %3D N SN = (In(2n + 1) – In(2n – 1)) . %3D n=1
n=1 ) Let a, = In(2n +1) – In(2n – 1). Does {an}1 converge or diverge? ) Let SN be the Nth partial sum of the series, i.e. %3D N SN = (In(2n + 1) – In(2n – 1)) . %3D n=1
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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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 {an}21 converge or diverge?
(b) Let SN be the Nth partial sum of the series, i.e.
N
SN = (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 Sn without sigma notation (i.e. expand the sum).
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