Question

1/(1 ? 2) + 1/(2 ? 3) + 1/(3 ? 4) + ….. + 1/{n(n + 1)} = ?​

Answer 1

Answer:

$\frac{n}{n + 1}$

Step-by-step explanation:

$\frac{1}{1} - \frac{1}{2} = \frac{1}{1 \times 2} \\ \frac{1}{2} - \frac{1}{3} = \frac{1}{2 \times 3} \\ \frac{1}{3} - \frac{1}{4} = \frac{1}{3 \times 4} \\ . \\ . \\ . \\ sum \: of \: all \\ \frac{1}{n} - \frac{1}{n + 1} = \frac{1}{n( n+ 1)} \\ \frac{1}{1} - \frac{1}{n + 1} = \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{n}{n + 1} \\ \frac{n}{ n+ 1} .$