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Summation of seriesAQA A-Level Further Maths: Mind map

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Other series
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Summation of series

standard results and differences

∑r\sum r∑r2\sum r^2∑r3\sum r^3
Method of differences
Worked ideas
Exam tips

Exam questions on Summation of series

  1. Let Sn=∑r=1nr(r+2)S_n=\sum_{r=1}^{n}r(r+2).
    Find the value of ∑r=1120r(r+2)\sum_{r=11}^{20}r(r+2).2 marks
  2. Let Un=∑r=1nr(r2−3)U_n=\sum_{r=1}^{n}r\left(r^2-3\right).
    Show that Un=14n(n+1)(n−2)(n+3)U_n=\frac14n(n+1)(n-2)(n+3).2 marks
  3. Let f(r)=r(r+1)(r+2)f(r)=r(r+1)(r+2).
    Show that f(r)−f(r−1)=3r(r+1)f(r)-f(r-1)=3r(r+1).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).