1/1.2.3+1/2.3.4+1/3.4.5+...+1/48.49.50

Đặt `A = 1/(1.2.3) + 1/(2.3.4) + 1/(3.4.5) + ..... + 1/(48.49.50)`

`=> 2A = 2/(1.2.3) + 2/(2.3.4) + 2/(3.4.5) + .... + 2/(48.49.50)`

`= 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ..... + 1/48.49 - 1/49.50`

`= 1/1.2 - 1/49.50`

`= 1/2 - 1/2450`

`= 612/1225`

`=> A = {612 : 2}/1225 = 306/1225`

Đáp án:

$\text{A =}$ `\frac{1}{1.2.3}` + `\frac{1}{3.4.5}` +...+ `\frac{1}{48.49.50}` 

$\text{A =}$ `\frac{1}{2}` . (`\frac{1}{2}` - `\frac{1}{2450}`)

$\text{A =}$ `\frac{1}{2}` . `\frac{612}{1225}`

$\text{A =}$ `\frac{306}{1225}`