Edexcel C2 2011 January — Question 5 4 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2011
SessionJanuary
Marks4
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TopicBinomial Theorem (positive integer n)
TypeRatio of coefficients condition
DifficultyModerate -0.8 Part (a) is trivial recall of the binomial coefficient formula (b=36). Part (b) requires writing the ratio of consecutive binomial coefficients and simplifying, which is a standard textbook exercise with minimal problem-solving. The calculation is straightforward: q/p = C(40,5)/C(40,4) = 36/5.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

  1. Given that \(\binom { 40 } { 4 } = \frac { 40 ! } { 4 ! b ! }\),
    1. write down the value of \(b\).
    In the binomial expansion of \(( 1 + x ) ^ { 40 }\), the coefficients of \(x ^ { 4 }\) and \(x ^ { 5 }\) are \(p\) and \(q\) respectively.
  2. Find the value of \(\frac { q } { p }\).

\begin{enumerate}
  \item Given that $\binom { 40 } { 4 } = \frac { 40 ! } { 4 ! b ! }$,\\
(a) write down the value of $b$.
\end{enumerate}

In the binomial expansion of $( 1 + x ) ^ { 40 }$, the coefficients of $x ^ { 4 }$ and $x ^ { 5 }$ are $p$ and $q$ respectively.\\
(b) Find the value of $\frac { q } { p }$.\\

\hfill \mbox{\textit{Edexcel C2 2011 Q5 [4]}}