OCR FP1 2008 January — Question 2 5 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and Series
TypeFinding Constants from Identity
DifficultyStandard +0.3 This is a straightforward Further Maths question requiring expansion of the sum using standard formulas (∑r² = n(n+1)(2n+1)/6 and ∑1 = n), then equating coefficients. While it involves algebraic manipulation and knowledge of summation formulas, it's a routine textbook exercise with a clear method and no novel insight required. Slightly above average difficulty due to being Further Maths content, but still mechanical.
Spec4.06a Summation formulae: sum of r, r^2, r^3

2 Given that \(\sum _ { r = 1 } ^ { n } \left( a r ^ { 2 } + b \right) \equiv n \left( 2 n ^ { 2 } + 3 n - 2 \right)\), find the values of the constants \(a\) and \(b\).

2 Given that $\sum _ { r = 1 } ^ { n } \left( a r ^ { 2 } + b \right) \equiv n \left( 2 n ^ { 2 } + 3 n - 2 \right)$, find the values of the constants $a$ and $b$.

\hfill \mbox{\textit{OCR FP1 2008 Q2 [5]}}