9231. FP1. Series. Past Exam Questions

November 2025 (9231/12). Question 1
- (a) Use standard results from the list of formulae (MF19) to find $\sum_{r=1}^{n} (r^3 - r)$ in terms of n, fully factorising your answer. [3 marks]
- (b) Express $\frac{r+3}{r^3-r}$ in the form $\frac{A}{r-1} + \frac{B}{r} + \frac{C}{r+1}$ , where A, B and C are constants to be determined, and hence use the method of differences to find $\sum_{r=2}^{n} \frac{r+3}{r^3 - r}$