Question 0521

Sigma Notation
2021 Paper 1 Question 5 Variant

Question

(a)
Express
x+8(x+4)(x+5)(x+6)\frac{x + 8}{(x + 4)(x + 5)(x + 6)}
in partial fractions.
[3]
(b)
Hence find, in terms of n,{n,}
r=1nr+8(r+4)(r+5)(r+6).\sum_{r=1}^n \frac{r + 8}{(r + 4)(r + 5)(r + 6)}.
[3]
(c)
State the value of
r=1r+8(r+4)(r+5)(r+6).\sum_{r=1}^\infty \frac{r + 8}{(r + 4)(r + 5)(r + 6)}.
[1]

Answer