Question 0521

Sigma Notation
2021 Paper 1 Question 5 Variant

Question

(a)
Express
4x+14(x+3)(x+4)(x+5)\frac{4 x + 14}{(x + 3)(x + 4)(x + 5)}
in partial fractions.
[3]
(b)
Hence find, in terms of n,{n,}
r=1n4r+14(r+3)(r+4)(r+5).\sum_{r=1}^n \frac{4 r + 14}{(r + 3)(r + 4)(r + 5)}.
[3]
(c)
State the value of
r=14r+14(r+3)(r+4)(r+5).\sum_{r=1}^\infty \frac{4 r + 14}{(r + 3)(r + 4)(r + 5)}.
[1]

Answer