Question 2 - A-Level Maths

Exam Board	AQA
Module	FP2 (Further Pure Mathematics 2)
Year	2009
Session	June
Topic	Sequences and series, recurrence and convergence

Given that $$\frac { 1 } { 4 r ^ { 2 } - 1 } = \frac { A } { 2 r - 1 } + \frac { B } { 2 r + 1 }$$ find the values of $A$ and $B$.
Use the method of differences to show that $$\sum _ { r = 1 } ^ { n } \frac { 1 } { 4 r ^ { 2 } - 1 } = \frac { n } { 2 n + 1 }$$
Find the least value of $n$ for which $\sum _ { r = 1 } ^ { n } \frac { 1 } { 4 r ^ { 2 } - 1 }$ differs from 0.5 by less than 0.001 .