Moderate -0.8 This is a straightforward application of standard summation formulae (∑r², ∑r, ∑1) with basic algebraic manipulation and factorisation. While it's Further Maths content, it requires only direct substitution of known formulae and routine algebraic simplification, making it easier than average even for FP1 students.
Obtain correct answer c.a.o. (Allow A1 for \(\frac{1}{2(2n^2+2)}\))
[7]
## Question 4:
| M1 | Express as sum of 3 series
| M1 | Use standard series results, at least 1 correct
| A1 | Two terms correct
$\frac{1}{2}n(n+1)(2n+1) - \frac{3}{2}n(n+1) + 2n$ | A1 | Third term correct
| M1 | Obtain factor of $n$
$n(n^2 + 1)$ | A2 | Obtain correct answer c.a.o. (Allow A1 for $\frac{1}{2(2n^2+2)}$)
**[7]**
---