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4 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 2 · Question 4(b)(iii)

A series is given as 2 + 3/4 + 4/9 + 5/16 + ...

Given that Σ(n=1 to ∞) (1/n²) converges, show that S_n diverges.

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Other parts of this question

  1. 4(a)(i)Obtain the Maclaurin series expansion for g up to the term in x⁴.[8 marks]
  2. 4(a)(ii)Hence, estimate g(2).[2 marks]
  3. 4(b)(i)Express the nᵗʰ partial sum S_n of the series using sigma notation.[2 marks]
  4. 4(b)(ii)Hence, calculate S₂₀ - S₁₈.[1 mark]
  5. 4(c)Use the method of induction to prove that Σ(r=1 to n) r(r-1) = n(n² - 1) / 3.[8 marks]

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