CAIE FP1 2014 November — Question 1

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and series, recurrence and convergence

1 Given that $$u _ { k } = \frac { 1 } { \sqrt { } ( 2 k - 1 ) } - \frac { 1 } { \sqrt { } ( 2 k + 1 ) }$$ express \(\sum _ { k = 13 } ^ { n } u _ { k }\) in terms of \(n\). Deduce the value of \(\sum _ { k = 13 } ^ { \infty } u _ { k }\).

1 Given that

$$u _ { k } = \frac { 1 } { \sqrt { } ( 2 k - 1 ) } - \frac { 1 } { \sqrt { } ( 2 k + 1 ) }$$

express $\sum _ { k = 13 } ^ { n } u _ { k }$ in terms of $n$.

Deduce the value of $\sum _ { k = 13 } ^ { \infty } u _ { k }$.

\hfill \mbox{\textit{CAIE FP1 2014 Q1}}