Question 8 - A-Level Maths

Exam Board	OCR
Module	FP1 (Further Pure Mathematics 1)
Year	2016
Session	June
Topic	Sequences and series, recurrence and convergence

Show that \(\frac { 1 } { 2 r + 1 } - \frac { 1 } { 2 r + 3 } \equiv \frac { 2 } { ( 2 r + 1 ) ( 2 r + 3 ) }\).
Hence find \(\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }\), giving your answer as a single fraction.
Find \(\sum _ { r = n } ^ { \infty } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }\), giving your answer as a single fraction.