Question

calculati S=1/2 +1/6+/12+1/20+.....1/90

Answer 1

$s = \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + ... + \frac{1}{90}$

$s = \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{4 \times 5} + ... + \frac{1}{9 \times 10}$

$s = \frac{2 - 1}{1 \times 2} + \frac{3 - 2}{2 \times 3} + \frac{5 - 4}{4 \times 5} + ... + \frac{10 - 9}{9 \times 10}$

$s = \frac{2}{1 \times 2} - \frac{1}{1 \times 2} + \frac{3}{2 \times 3} - \frac{2}{2 \times 3} +$

$\frac{5}{4 \times 5} - \frac{4}{4 \times 5} + ... + \frac{10}{9 \times 10} - \frac{9}{9 \times 10}$

$s = \frac{ 1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - ... - \frac{1}{10}$

$s = 1 - \frac{1}{10}$

$s = \frac{10}{10} - \frac{1}{10}$

$s = \frac{9}{10}$