Question 0510

Sigma Notation
2010 Paper 2 Question 2 Variant

Question

(a)
Prove by the method of differences that
r=5n1(r2)r=72412n212n.\sum_{r=5}^n \frac{1}{(r - 2) r} = \frac{7}{24} - \frac{ 1 }{ 2 n - 2 } - \frac{ 1 }{ 2 n }.
[4]
(b)
Explain why r=51(r2)r{\displaystyle \sum_{r=5}^\infty \frac{1}{(r - 2) r}} is a convergent series, and state the value of the sum to infinity.
[2]

Answer