Question 9 - A-Level Maths

Exam Board	OCR
Module	FP1 (Further Pure Mathematics 1)
Year	2013
Session	June
Topic	Sequences and series, recurrence and convergence

Show that \(\frac { 1 } { 3 r - 1 } - \frac { 1 } { 3 r + 2 } \equiv \frac { 3 } { ( 3 r - 1 ) ( 3 r + 2 ) }\).
Hence show that \(\sum _ { r = 1 } ^ { 2 n } \frac { 1 } { ( 3 r - 1 ) ( 3 r + 2 ) } = \frac { n } { 2 ( 3 n + 1 ) }\).