An equation in binomial coefficients

An equation in binomial coefficients

Secondary 3

Do not use a calculator in this question.

  1. Given that \(\binom n2=2\binom n1+12\), where \(n\) is a positive integer, find the value of \(n\).
  2. Hence find the coefficient of \(x^2\) in the expansion of \((1+2x)^n\).

Solution:

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Answer:(a) \(n=8\) (b) \(112\)

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