Question 2 - A-Level Maths

Exam Board	SPS
Module	SPS FM (SPS FM)
Year	2022
Session	November
Topic	Sequences and series, recurrence and convergence

Show that $\frac { 1 } { \sqrt { r + 2 } + \sqrt { r } } \equiv \frac { \sqrt { r + 2 } - \sqrt { r } } { 2 }$.
Hence find an expression, in terms of $n$, for $$\sum _ { r = 1 } ^ { n } \frac { 1 } { \sqrt { r + 2 } + \sqrt { r } }$$
State, giving a brief reason, whether the series $\sum _ { r = 1 } ^ { \infty } \frac { 1 } { \sqrt { r + 2 } + \sqrt { r } }$ converges.
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