Tính `1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132+1/156+1/182+1/210+1/240+1/272`

Đáp án:

Giải thích các bước giải:

 `1 + 1/2 + 1/6 + 1/12 + … + 1/240 + 1/272`

`= 1 + 1/(1 . 2) + 1/(2 . 3) + ..+ 1/(15 . 16) + 1/(16 . 17)`

`= 1 + (2 – 1)/(1 . 2) + (3 – 2)/(2 . 3) + ..+ (16 – 15)/(15 . 16) + (17 – 16)/(16 . 17)`

`= 1 + 1 – 1/2 + 1/2 – 1/3 + 1/3 – ….+ 1/15 – 1/16 + 1/16 – 1/17`

`= 1 + 1 – 1/17`

`= 2 – 1/17`

`= 34/17 – 1/17`

`= 33/17`