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Binomial expansion with unknown index and coefficient found from the first three terms

Binomial expansion with unknown index and coefficient found from the first three terms

6 marks

Given that \((1+bx)^n=1+6x+16x^2+\cdots\), where \(n\) is a positive integer and \(b\) is a constant, find

  1. the value of \(n\) and the value of \(b\),[4]
  2. the term in \(x^4\).[2]

Solution:

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Answer:(a) \(n=9,\ b=\frac23\) (b) \(\frac{224}{9}x^4\)

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