Standard +0.3 This is a straightforward proof by induction of a summation formula with standard structure: verify base case n=1, assume true for n=k, prove for n=k+1 by algebraic manipulation. The algebra is routine (expanding and factoring quadratics) and requires no novel insight, making it slightly easier than average despite being a Further Maths topic.
Show sufficient working to verify result true when \(n=1\)
\(k(k+1)^2 + (k+1)(3k+4)\)
M1*
Add next term in series
DM1
Attempt to factorise their expression
\((k+1)(k+2)^2\)
A1
Sufficient working to obtain this correct answer
B1
Clear statement of induction process, provided previous 4 marks earned
[5]
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1 | Show sufficient working to verify result true when $n=1$ |
| $k(k+1)^2 + (k+1)(3k+4)$ | M1* | Add next term in series |
| | DM1 | Attempt to factorise their expression |
| $(k+1)(k+2)^2$ | A1 | Sufficient working to obtain this correct answer |
| | B1 | Clear statement of induction process, provided previous 4 marks earned |
| **[5]** | | |
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