Moderate -0.3 This is a straightforward summation question requiring expansion to r²-1, then applying standard summation formulas. While it's FP1, the technique is mechanical and the factorisation at the end is routine, making it slightly easier than an average A-level question despite being Further Maths content.
Answer: \(\frac{1}{6}n(n+1)(2n+1)-n\) or \(\frac{1}{6}n(2n+5)(n-1)\)
M1*, DM1, A1; DM1, A2 [6]
Attempt to expand \((r-1)(r+1)\); Use standard result for \(\sum r^2\); Obtain correct unsimplified answer; Attempt to factorise; Obtain completely correct answer. Allow A1 if one bracket still contains a common factor
Answer: $\frac{1}{6}n(n+1)(2n+1)-n$ or $\frac{1}{6}n(2n+5)(n-1)$ | M1*, DM1, A1; DM1, A2 [6] | Attempt to expand $(r-1)(r+1)$; Use standard result for $\sum r^2$; Obtain correct unsimplified answer; Attempt to factorise; Obtain completely correct answer. Allow A1 if one bracket still contains a common factor