Find the sum to $n$ terms of the series $\large\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+..........$

Question

$\begin{array}{1 1} \large\frac{n}{n+1} \\ \large\frac{n-1}{n+1} \\\large\frac{1}{n+1} \\ \large\frac{1}{n(n+1)}\end{array}$