- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
- Show that, for \(r \geqslant 2\)
$$\frac { 2 } { \sqrt { r } + \sqrt { r - 2 } } = \sqrt { r } - \sqrt { r - 2 }$$
- Hence use the method of differences to determine
$$\sum _ { r = 2 } ^ { n } \frac { 2 } { \sqrt { r } + \sqrt { r - 2 } }$$
giving your answer in simplest form.
- Hence show that
$$\sum _ { r = 4 } ^ { 50 } \frac { 2 } { \sqrt { r } + \sqrt { r - 2 } } = A + B \sqrt { 2 } + C \sqrt { 3 }$$
where \(A\), \(B\) and \(C\) are integers to be determined.