Porisma

A hint to get started

Rewrite before choosing ascending powers

Expand the following in ascending powers of x. Find the range of values of x for which the series expansion is valid.

(i) (8+x)1/3(8+x)^{1/3}, up to and including the term in x2x^2.

(ii) (1−1/x)−1(1-1/x)^{-1}, up to and including the term in x4x^4.

CJC · Lecture · Example 3

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