Question 1 - A-Level Maths

Exam Board	Edexcel
Module	FP2 (Further Pure Mathematics 2)
Year	2014
Session	June
Topic	Sequences and series, recurrence and convergence

(a) Express $\frac { 2 } { 4 r ^ { 2 } - 1 }$ in partial fractions.
(b) Hence use the method of differences to show that

$$\sum _ { r = 1 } ^ { n } \frac { 1 } { 4 r ^ { 2 } - 1 } = \frac { n } { 2 n + 1 }$$