Question 0515

Sigma Notation
2015 Paper 2 Question 4 Variant

Question

(i)
Show that 24r2+16r+15{\displaystyle \frac{2}{4 r^2 + 16 r + 15}} can be expressed as A2r+3+B2r+5,{\displaystyle \frac{A}{2 r + 3} + \frac{B}{2 r + 5},} where A{A} and B{B} are constants to be determined.
[1]
The sum r=2n24r2+16r+15{\displaystyle \sum_{r=2}^n \frac{2}{4 r^2 + 16 r + 15}} is denoted by Sn.{S_n.}
(ii)
Find an expression for Sn{S_n} in terms of n.{n.}
[4]
(iii)
Find the smallest values of n{n} for which Sn{S_n} is within 104{10^{-4}} of the sum to infinity.
[3]

Answer