Cancellation and first non-zero terms

Cancellation and first non-zero terms

IB Year 5 | Grade 11
5 marks

Find the first three non-zero terms in the expansion of \((1-x)(1+2x)^{1/2}\), and state its standard open range of validity.[5]

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Answer:\(1-\frac32x^2+x^3+\cdots;\ |x|<\frac12\)

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