# Some one help me find A, know A = 1/1xx2xx3 + 1/2xx3xx4 + 1/3xx4xx5 +...+ 1/8xx9xx10 ?

May 5, 2018

$\implies A = \frac{9161}{140}$

#### Explanation:

The terms listed:

$\frac{1}{1} \times 2 \times 3 = 6$

$\frac{1}{2} \times 3 \times 4 = 6$

$\frac{1}{3} \times 4 \times 5 = \frac{20}{3}$

$\frac{1}{8} \times 9 \times 10 = \frac{45}{4}$

The terms not listed:

$\frac{1}{4} \times 5 \times 6 = \frac{15}{2}$

$\frac{1}{5} \times 6 \times 7 = \frac{42}{5}$

$\frac{1}{6} \times 7 \times 8 = \frac{28}{3}$

$\frac{1}{7} \times 8 \times 9 = \frac{72}{7}$

Summing all terms:

$A = 6 + 6 + \frac{20}{3} + \frac{15}{2} + \frac{42}{5} + \frac{28}{3} + \frac{72}{7} + \frac{45}{4}$

$A = 12 + \frac{15}{2} + \frac{48}{3} + \frac{45}{4} + \frac{42}{5} + \frac{72}{7}$

$A = \frac{39}{2} + \frac{48}{3} + \frac{45}{4} + \frac{42}{5} + \frac{72}{7}$

If you continue to find common denominators and sum you will arrive at:

$\implies A = \frac{9161}{140}$