Moderate -0.3 This is a straightforward application of standard summation formulae requiring expansion of r²(r-1) = r³ - r², then applying the known formulae for Σr³ and Σr². The algebraic manipulation and factorisation at the end is routine. While it's a Further Maths question, it's a standard textbook exercise with no novel insight required, making it slightly easier than average overall.
$\frac{1}{4}n^2(n+1)^2 - \frac{1}{6}n(n+1)(2n+1)$ | M1 | Express as difference of two series
| M1 | Use standard results
| A1 | Correct unsimplified answer
$\frac{1}{12}n(n+1)(3n+2)(n-1)$ | M1 | Attempt to factorise
| A1 | At least factor of $n(n+1)$
| A1 | Obtain correct answer
| **6 marks**