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The method of differencesEdexcel International A Level Further Maths: Mind map

The idea
Partial fractions
Gaps

Method of differences

telescoping series

f(r)−f(r+1)partial fractionscancel
Other series
Infinity
Exam tips

Exam questions on The method of differences

  1. The general term of a series is ur=1r(r+2)u_r=\frac{1}{r(r+2)} for r≥1r\ge1.
    Find ∑r=1∞ur\sum_{r=1}^{\infty}u_r.2 marks
  2. Let f(r)=r!f(r)=r! for positive integers rr.
    Hence find ∑r=35r⋅r!\sum_{r=3}^{5}r\cdot r!.2 marks
  3. A series has general term ur=1(2r−1)(2r+1)u_r=\frac{1}{(2r-1)(2r+1)} for r≥1r\ge1.
    Express uru_r in partial fractions.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).