I have a result for part a) which is

1+(3/2*x)+((27/16)*x^2)+((27/16)*x^3)+......

using this and the fact that 1-3x=4-3(x+1) i need to find a taylor series for

g(x) =[16/(1-3x)^2]

I know its by substitution but I just don't know where to start.

I did post part a of this question but I was confident in what I was doing - this I haven't got clue as once I have resolved this I need to check first four terms in the Taylor series by finding first, second and third derivatives.