Chapter 12.4, Problem 11AYU

In Problems 1-22, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers $n$.

$\frac{1}{1\cdot 2}\text{ + }\frac{1}{2\cdot 3}\text{ + }\frac{1}{3\cdot 4}\text{ + }\mathrm{...}\text{ + }\frac{1}{n\left(n\text{ + 1}\right)}\text{ = }\frac{n}{n+1}$