CAIE FP1 2016 November — Question 1

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and series, recurrence and convergence

1 Use the method of differences to find \(\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r ) ^ { 2 } - 1 }\). Deduce the value of \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r ) ^ { 2 } - 1 }\).

1 Use the method of differences to find $\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r ) ^ { 2 } - 1 }$.

Deduce the value of $\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r ) ^ { 2 } - 1 }$.

\hfill \mbox{\textit{CAIE FP1 2016 Q1}}