Limit of an Exponential Expression

Find the limit of ${\left\{{\left(\frac{n+1}{n}\right)}^n-\frac{n+1}{n}\right\}}^{-n}$ as $n$ approaches infinity.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XX. Limiting Values and Vanishing Fractions, Examples XX, No. 16