Question

tính tổng : A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56

Answer 1

`= 1 - 1/2 + 1 - 1/6 + ... + 1 - 1/56`

`= 1 - 1/(1.2) + 1 - 1/(2.3) + ... + 1 - 1/(7.8)`

`= 7 - (1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4+ 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8`.

`= 8 - 1/8`

`= 63/64`.

Answer 2

`A=1/2+5/6+11/12+19/20+29/30+41/42+55/56`

`A=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56`

`A=(1+1+1+1+1+1+1)-(1/2+1/6+1/12+....+1/56)`

`A=7-(1/[1xx2]+1/[2xx3]+1/[3xx4]+....+1/[7xx8])`

`A=7-(1-1/2+1/2-1/3+1/3-1/4+....+1/7-1/8)`

`A=7-(1-1/8)`

`A=7-(8/8-1/8)`

`A=7-7/8`

`A=56/8-7/8=49/8`