1/2 + 1/6 + 1/12 + 1/20 + 1/30 Các bạn giải chi tiết giúp mình nha.

`1/2 + 1/6 + 1/12 + 1/20 + 1/30`

Ta có: `1/2 = 1 – 1/2`

`1/6 = 1/2 – 1/3`

`1/12 = 1/3 – 1/4`

`1/20 = 1/4 – 1/5`

`1/30 = 1/5 – 1/6`

`⇒ 1/2 + 1/6 + 1/12 + 1/20 + 1/30= 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6`

`= 1 – (-1/2 + 1/2) + (-1/3 + 1/3) + (-1/4 + 1/4) + (-1/5 + 1/5) + -1/6`

`= 1 – 1/6`

`= 6/6 – 1/6`

`= 5/6`