| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2014 |
|---|
| Session | November |
|---|
| Topic | Sequences 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 \(\sum _ { k = 13 } ^ { \infty } u _ { k }\).