5 marksThe Real Number System – ℝ
CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 1(c)(i)
Show that Σ (from r=1 to n) r(r + 1) = (1/3)n(n + 1)(n + 2), n ∈ N.
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Practise this questionOther parts of this question
- 1(a)Find the values of the real constants p, q and r.[7 marks]
- 1(b)(i)Without using calculators or tables, show that (√6 + √2) / (√6 - √2) = 2 + √3.[5 marks]
- 1(b)(ii)Without using calculators or tables, show that (√6 + √2) / (√6 - √2) + (√6 - √2) / (√6 + √2) = 4.[5 marks]
- 1(c)(ii)Hence, or otherwise, evaluate Σ (from r=31 to 50) r(r + 1).[3 marks]
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