CAIE A-Level Further Math 1.3.1 Standard series sums

Practise using MF19 standard sums to turn polynomial expressions in r into simplified formulae in n, including factorised forms.

Exam points

expand polynomial terms in r before substituting MF19 formulae for Σr, Σr² and Σr³
fully factorise a sum in n when the final form, rather than expansion, is requested

[Maximum number: 3]

Use standard results from the list of formulae (MF19) to find $\sum_{r=1}^{n}\left(3 r^{2}+3 r+1\right)$ in terms of n, simplifying your answer.

$\frac{1}{2} n(n+1)(2 n+1)+\frac{3}{2} n(n+1)+n$

M1 A1

Substitutes correct formulae from
MF19.

$n^{3}+3 n^{2}+3 n$

A1

Simplifies

3

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