CAIE FP1 2019 November — Question 4

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2019
SessionNovember
TopicSequences and series, recurrence and convergence

4 The line \(y = 2 x + 1\) is an asymptote of the curve \(C\) with equation $$y = \frac { x ^ { 2 } + 1 } { a x + b }$$
  1. Find the values of the constants \(a\) and \(b\).
  2. State the equation of the other asymptote of \(C\).
  3. Sketch C. [Your sketch should indicate the coordinates of any points of intersection with the \(y\)-axis. You do not need to find the coordinates of any stationary points.]
    \(5 \quad\) Let \(S _ { N } = \sum _ { r = 1 } ^ { N } ( 5 r + 1 ) ( 5 r + 6 )\) and \(T _ { N } = \sum _ { r = 1 } ^ { N } \frac { 1 } { ( 5 r + 1 ) ( 5 r + 6 ) }\).