Question

For \(n \geq 1\) set \( f(x) = \frac{1}{(1-x)^{n+1} }\) . Calculate the power series expansion of \(f\) at \(x_{0} = 0\) by two different ways:
b) Realise \(f\) as an \(n-th\) derivative of a "known" function \(g\), and then differentiate the power series of \(g\) term wise \(n\) times.