Past exam of the mathematical methods II course of the University of Oxford / 2014 resit / 2 / b

Use the Maclaurin series $\ln (1+x)=x-x^2/2+x^3/3+O(x^4)$ and the geometric series $(1+y{)}^{-1}=1-y+y^2-y^3+\cdots$. Multiplication, grouped by total degree, givesThe six displayed nonzero terms include every contribution through total degree three. A sufficient open region for the convergent product expansion is $|x|<1$, $|y|<1$.