What is the value of $$\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + \dots + \frac{2}{45 \times 47}$$ ?​

Correct option is A

Solution:

$$\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + \dots + \frac{2}{45 \times 47}$$ 

$$\frac{2}{n \times (n+2)} = \frac{2}{2} \left( \frac{1}{n} - \frac{1}{n+2} \right)$$ 

$$\left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \dots + \left( \frac{1}{45} - \frac{1}{47} \right)$$ 

$$1 - \frac{1}{47} = \frac{46}{47}$$​