Pearson Edexcel IAL Mathematics FP2.2 Series Question Bank

Practise summing finite and limiting series by rewriting terms, using differences, and expressing answers in required algebraic forms.

Exam points

use partial fractions to create cancelling terms in a finite sum
apply the method of differences to obtain a formula in n or an exact finite value

Covered syllabus points

FP2.2.1 - Summation of simple finite series n 1 ∑

[Maximum number: 4]

Hence, using the method of differences, show that for all integer values of n,

\sum_{r=1}^{n} \frac{1}{(2 r-1)(2 r+1)(2 r+3)}=\frac{n(n+2)}{a(2 n+b)(2 n+c)}

where a, b and c are integers to be determined.

$\frac18\sum_{r=1}^{n}\left(\frac{1}{2r-1}-\frac{2}{2r+1}+\frac{1}{2r+3}\right)$ $=\frac18\left(1-\frac13-\frac{1}{2n+1}+\frac{1}{2n+3}\right)$ $=\frac18\left(\frac{2(2n+1)(2n+3)-3(2n+3)+3(2n+1)}{3(2n+1)(2n+3)}\right)$ $=\frac{n(n+2)}{3(2n+1)(2n+3)}$
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Covered syllabus points

FP2.2 - Series question 1