Mọi người giúp em với ạ. Em cảm ơn Bài 1 : Tính nhanh a) 1/1 . 1/2 + 1/2 . 1/3 + 1/3 . 1/4 + 1/4 .1/5 b) 1/2+1/6+1/12+1/20+1/30 c) 1/2+1/6+1/12+.......+1/10100 d) 2/1.3 +2/3.5 + 2/5.7 +.........+2/99.100

`a)`

`1/1 . 1/2 + 1/2 . 1/3 + 1/3 . 1/4 + 1/4 . 1/5`

`= 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + 1/(4 . 5)`

`= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5`

`= 1/1 - 1/5`

`= 4/5`

`b)`

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

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

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

`= 1/1 - 1/6`

`= 5/6`

`c)`

`1/2 + 1/6 + 1/12 + ... + 1/10100`

`= 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/(100 . 101)`

`= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/100 + 1/100 - 1/101`

`= 1/1 - 1/101`

`= 100/101`

`d)`

`2/(1 . 3) + 1/(3 . 5) + 5/(5 . 7) + ... + 2/(99 . 101)`

`= 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 + 1/99 + 1/101`

`= 1/1 - 1/101`

`= 100/101`