Question

please solve this question​

Answer 1

Step-by-step explanation:

$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{1}{100 \times 101} \\ = \frac{2 - 1}{2 \times 1} + \frac{3 - 2}{3 \times 2} + \frac{4 - 3}{4 \times 3} + ... + \frac{101 - 100}{101 \times 100} \\ = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{100} - \frac{1}{101} \\ = 1 - \frac{1}{101} \\ = \frac{101 - 1}{101} \\ = \frac{100}{101}$

The answer is option b.

Thank you