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2 marksNumber Sequences and Rules

CSEC Mathematics · January 2008 · Paper 2 · Question 8(b)(ii)

The student observed a pattern: 1^3+2^3+3^3=36 = 6^2 and 1^3+2^3+3^3+4^3=100 = 10^2.

Using the pattern observed in these two statements, determine the sum of the series: 1^3 + 2^3 + 3^3 + ... + n^3.

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Other parts of this question

  1. 8(a)(i)Complete the row for n=6 in the table.[3 marks]
  2. 8(a)(ii)Complete the row for n in the table.[2 marks]
  3. 8(b)(i)Using the pattern observed in these two statements, determine the sum of the series: 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3[1 mark]
  4. 8(c)Hence, or otherwise, determine the EXACT value of the sum of the series: 1^3 + 2^3 + 3^3 + 4^3 + ... + 12^3[2 marks]

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