Find the sum : $$\frac{1}{2} + $$ $$\frac{1}{6} + $$ $$\frac{1}{{12}} + $$ $$\frac{1}{{20}} + $$ $$\frac{1}{{30}} + $$ $$\frac{1}{{42}} + $$ $$\frac{1}{{56}} + $$ $$\frac{1}{{72}} + $$ $$\frac{1}{{90}} + $$ $$\frac{1}{{110}} + $$ $$\frac{1}{{132}}$$ $$ = ?$$

Find the sum : $$\frac{1}{2} + $$ $$\frac{1}{6} + $$ $$\frac{1}{{12}} + $$ $$\frac{1}{{20}} + $$ $$\frac{1}{{30}} + $$ $$\frac{1}{{42}} + $$ $$\frac{1}{{56}} + $$ $$\frac{1}{{72}} + $$ $$\frac{1}{{90}} + $$ $$\frac{1}{{110}} + $$ $$\frac{1}{{132}}$$ $$ = ?$$ Correct Answer $$\frac{{11}}{{12}}$$

Given expression,
 $${\text{ = }}\left( {1 - \frac{1}{2}} \right)$$   $$ + $$ $$\left( {\frac{1}{2} - \frac{1}{3}} \right)$$   $$ + $$ $$\left( {\frac{1}{3} - \frac{1}{4}} \right)$$   $$ + $$ $$\left( {\frac{1}{4} - \frac{1}{5}} \right)$$   $$ + $$ . . . . . $$ + $$ $$\left( {\frac{1}{{11}} - \frac{1}{{12}}} \right)$$
$$\eqalign{ & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}} \cr} $$