Challenging Maclaurin’s series problem 1

If ,

(i) find the Maclaurin’s series of f(x) up to and including the term in .

(ii) Hence deduce the series expansion of the function  up to and including the term in 

Solution

(i) is routine, can easily work out to be

(ii) requires Higher Order Thinking (HOT)

We differentiate the series obtained in (i) to get 

Principle used: Differentiate one series expansion to get the series expansion for another series.