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A hint to get started

Practise finite and nonterminating binomial expansions

Expand the following as a series in ascending powers of x, up to and including the term in x3x^3, stating the set of values of x for which the expansion is valid.

(a) (4+x)4(4+x)^4

(b) (1/x+1)−2(1/x+1)^{-2}

(c) (x+4)−3/2(x+4)^{-3/2}

CJC · Lecture · Self-Practice 1

Make the bracket start with 1, choose ascending powers of x, and transform the convergence condition while retaining the original domain.

Read the worked solution