Standard +0.3 This is a standard textbook proof by induction of a well-known summation formula. The algebraic manipulation in the inductive step is straightforward (factoring a cubic), and this exact question appears in most Further Pure textbooks as a foundational example. While it requires understanding of induction structure, it demands no novel insight and is slightly easier than average due to its routine nature.
Attempt to factorise or expand and simplify; Correct expression obtained
(Specific statement of induction conclusion, with no errors seen)
A1
5 marks total
$1^2 = \frac{1}{6} \times 1 \times 2 \times 3$ | B1 | Show result true for $n = 1$ or $2$
$\frac{1}{6}n(n+1)(2n+1) + (n+1)^2$ | M1 | Add next term to given sum formula, any letter OK
$\frac{1}{6}(n+1)(n+2)(2(n+1)+1)$ | DM1 A1 | Attempt to factorise or expand and simplify; Correct expression obtained
(Specific statement of induction conclusion, with no errors seen) | A1 | 5 marks total