Chapter 1.8, Problem 70ES

Let $f\left(x\right)={\left(1+\frac{1}{x}\right)}^x$ .

(a) Prove the identity $f\left(-x\right)=\frac{x}{x-1}\cdot f\left(x-1\right)$

(b) Use Equation (d) and the identity form part (a) to prove Equation (5).