Ta có :

`A=  1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42`

`A= 1/(1xx2) + 1/(2xx3) + 1/(3xx4) + 1/(4xx5) + 1/(5xx6) + 1/(6xx7)`

`A=  1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7`

`A = 1-1/7`

`A=  6/7`

Ta có :

`1 = 7/7`

`6/7` giữ nguyên

Vì `6<7` nên `6/7 < 7/7`

Hay `A<1`

Vậy `A<1` ( dpcm )