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2026 NYGH P2 Q11

2026 NYGH P2 Q11

IP 4
11 marks
  1. Find the term independent of \(x\) in the expansion of \(\left(3x+\dfrac1{2x^2}\right)^9\).[4]
    1. Find the first three terms, in ascending powers of \(x\), in the expansion of \(\left(1-\dfrac x3\right)^n\), where \(n\) is a positive integer.[2]
    2. The coefficient of \(x^2\) in the expansion of \((1+3x)\left(1-\dfrac x3\right)^n\) is \(-5\). Find the possible values of \(n\).[5]

Solution:

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Answer:(a) \(7654.5\) (b)(i) \(1-\dfrac{nx}{3}+\dfrac{n(n-1)x^2}{18}\) (b)(ii) \(n=9,10\)

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