Question

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

Answer 1

`=>A = 9161/140`

Explanation:

The terms listed:

`1/1 xx 2 xx 3 = 6`

`1/2 xx 3 xx 4 = 6`

`1/3 xx 4 xx 5 = 20/3`

`1/8 xx 9 xx 10 = 45/4`

The terms not listed:

`1/4 xx 5 xx 6 = 15/2`

`1/5 xx 6 xx 7 = 42/5`

`1/6 xx 7 xx 8 = 28/3`

`1/7 xx 8 xx 9 = 72/7`

Summing all terms:

`A = 6+6+20/3+15/2+42/5+28/3+72/7+45/4`

`A = 12 + 15/2 + 48/3 + 45/4 + 42/5 + 72/7`

`A = 39/2 + 48/3 + 45/4 + 42/5 + 72/7`

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

`=>A = 9161/140`