Question 7 - A-Level Maths

Exam Board	OCR
Module	FP1 (Further Pure Mathematics 1)
Year	2011
Session	June
Topic	Sequences and series, recurrence and convergence

Show that \(\frac { 1 } { r - 1 } - \frac { 1 } { r + 1 } \equiv \frac { 2 } { r ^ { 2 } - 1 }\).
Hence find an expression, in terms of \(n\), for \(\sum _ { r = 2 } ^ { n } \frac { 2 } { r ^ { 2 } - 1 }\).
Find the value of \(\sum _ { r = 1000 } ^ { \infty } \frac { 2 } { r ^ { 2 } - 1 }\).