A fractional power after factorisation

A fractional power after factorisation

IB Year 5 | Grade 11
6 marks

Find the first four non-zero terms in the expansion of \(\sqrt{4+3x}\) in ascending powers of \(x\), and state the standard open range of validity.[6]

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Answer:\(2+\frac34x-\frac9{64}x^2+\frac{27}{512}x^3+\cdots;\ -\frac43<x<\frac43\)

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