Removing a linear term

Removing a linear term

IB Year 5 | Grade 11
6 marks

The coefficient of \(x\) in \((1+px)(1-4x)^{-1/2}\) is zero. Find \(p\) and the first three non-zero terms of the expansion. State the standard open range of validity.[6]

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Answer:\(p=-2;\ 1+2x^2+8x^3+\cdots;\ |x|<\frac14\)

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