What is the value of
​$$\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + \dots + \frac{2}{99 \times 101}$$ ​

Correct option is C

Solution:

​$$\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + \dots + \frac{2}{99 \times 101}\\\ \\ 1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} ............ + \frac{1}{97} - \frac{1}{99} +\frac{1}{99} - \frac{1}{101} \\\ \\$$

$$= \left( 1 - \frac{1}{101} \right) \\\ \\ = \frac{100}{101}$$​​​