Question 0521

Sigma Notation
2021 Paper 1 Question 5 Variant

Question

(a)
Express
5x+26(x+4)(x+5)(x+6)\frac{5 x + 26}{(x + 4)(x + 5)(x + 6)}
in partial fractions.
[3]
(b)
Hence find, in terms of n,{n,}
r=1n5r+26(r+4)(r+5)(r+6).\sum_{r=1}^n \frac{5 r + 26}{(r + 4)(r + 5)(r + 6)}.
[3]
(c)
State the value of
r=15r+26(r+4)(r+5)(r+6).\sum_{r=1}^\infty \frac{5 r + 26}{(r + 4)(r + 5)(r + 6)}.
[1]

Answer