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7 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 3(b)(i)

The n-th partial sum of a series, S_n, is given by S_n = sum_{r=1}^n r(r - 1).

Show that S_n = (n(n^2 - 1)) / 3.

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Other parts of this question

  1. 3(a)Given that u_8 = 13x + 1 and that u_10 = 34x + 1, find (u_9)'.[4 marks]
  2. 3(b)(ii)Hence, or otherwise, evaluate sum_{r=10}^20 r(r - 1).[5 marks]
  3. 3(c)(i)Given that ^n P_r = n! / (n - r)!, show that (^2r P_r * ^n P_r) / ((2r)!) is equal to the binomial coefficient ^n C_r.[4 marks]
  4. 3(c)(ii)Determine the coefficient of the term in x^3 in the binomial expansion of (3x + 2)^5.[5 marks]

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