Standard +0.3 This is a standard textbook induction proof with a given formula to verify. The algebraic manipulation in the inductive step is straightforward—factoring n²(n+1)² and showing (n+1)³ fits the pattern. While it's Further Maths content, it's one of the most routine induction questions possible, requiring only mechanical execution of the standard method with minimal algebraic challenge.
Add next term to given sum formula. Attempt to factorise and simplify.
\(\frac{1}{4}(n+1)^2(n+2)^2\)
A1
Correct expression obtained convincingly.
5
Specific statement of induction conclusion.
Total: 5 marks
$(1^3 =) \frac{1}{4} \times 1^2 \times 2^2$ | B1 | Show result true for $n = 1$. |
$\frac{1}{4}n^2(n+1)^2 + (n+1)^3$ | M1 M1(indep) | Add next term to given sum formula. Attempt to factorise and simplify. |
$\frac{1}{4}(n+1)^2(n+2)^2$ | A1 | Correct expression obtained convincingly. |
| | 5 | Specific statement of induction conclusion. |
**Total: 5 marks**