• This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\left( \begin{gathered} 3k + 1 \\\ 3k - 2 \end{gathered} \right) = \frac{{\left( {3k + 1} \right)!}}{{\left( {3k - 2} \right)!3!}}$ (M1)

$= \frac{{\left( {3k + 1} \right)3k\left( {3k - 1} \right)}}{{3!}}$ A1

$= \frac{9}{2}{k^3} - \frac{1}{2}k$ or equivalent A1

[3 marks]

attempt to solve$= \frac{9}{2}{k^3} - \frac{1}{2}k > {10^6}$ (M1)

$k > 60.57 \ldots$ (A1)

Note: Allow equality.

$\Rightarrow k = 61$ A1

[3 marks]