9758/2021/P1/Q05

(a) Express $\frac{x}{(x+2)(x+3)(x+4)}$ in partial fractions.

[3]

(b) Hence find, in terms of $n, \sum_{r=1}^n \frac{r}{(r+2)(r+3)(r+4)}$.

[3]

(c) State the value of $\sum_{i=1}^{\infty} \frac{r}{(r+2)(r+3)(r+4)}$.

[1]