Question 8 - A-Level Maths

Exam Board	OCR
Module	FP1 (Further Pure Mathematics 1)
Year	2012
Session	January
Topic	Sequences and series, recurrence and convergence

Show that $\frac { r } { r + 1 } - \frac { r - 1 } { r } \equiv \frac { 1 } { r ( r + 1 ) }$.
Hence find an expression, in terms of $n$, for $$\frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 } + \ldots + \frac { 1 } { n ( n + 1 ) }$$
Hence find $\sum _ { r = n + 1 } ^ { \infty } \frac { 1 } { r ( r + 1 ) }$.