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Sums of seriesEdexcel A-Level Further Maths: Mind map

Standard results
Method

Sums of series

standard results

∑r\sum r∑r2\sum r^2∑r3\sum r^3
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Worked results
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Exam questions on Sums of series

  1. A student uses the standard summation formulae for the first nn positive integers, their squares and their cubes.
    Find the value of ∑r=112r3\sum_{r=1}^{12}r^3.2 marks
  2. Let Sn=∑r=1n(r2+r)S_n=\sum_{r=1}^{n}\left(r^2+r\right).
    Hence find the value of ∑r=1120(r2+r)\sum_{r=11}^{20}\left(r^2+r\right).2 marks
  3. Let f(n)=∑r=1nr(r2+2)f(n)=\sum_{r=1}^{n}r\left(r^2+2\right).
    Show that f(n)=14n(n+1)(n2+n+4)f(n)=\frac14n(n+1)\left(n^2+n+4\right).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).