First, convert the problem to a slightly different form: \(\frac{1}{(a+b)^n} = \frac{1}{b^n} \frac{1}{(\frac{a}{b}+1)^n} = \frac{1}{b^n} \sum_{k=0}^{\infty} {(-1)^k \binom{n + k - 1}{k} \left ( \frac{a}{b} \right ) ^k}\)