M=10/56+10/140+10/260+...+10/1400 NHANH HỘ EM VỚI Ạ (AI nhanh đc ctrlhn)

`M=10/56 + 10/140 + ... +10/1400`

`= 5/28 + 5/70 + ... + 5/700`

`= 5/(4.7) + 5/(7.10) + ... + 5/(25.28)`

`=  5 (1/(4.7) + 1/(7.10)+...+1/(25.28))`

`= 5 . 1/3 . (1/4 - 1/7 +1/7 - 1/10 + ... +1/25 - 1/28)`

`= 5/3 . (1/4 - 1/28)`

`=5/3 . (7/28 - 1/28)`

`= 5/3 . 6/28`

`=5/14`

Vậy `M=5/14`

Đáp án:

 `M =5/14` 

Giải thích các bước giải:

`M =10/56+10/140+10/260 +...+10/1400`

`-> M =5/28 + 5/70+5/130 + ... +5/700`

`-> M = 5/(4 . 7) + 5/(7 . 10)+ 5/(10 . 13) +... + 5/(25 . 28)`

`-> M = 5/3( 3/(4 . 7) +3/(7.10)+ 3/(10 . 13)+...+3/(25 . 28))`

`-> M =5/3(1/4 -1/7+1/7-1/10+1/10-1/13+...+1/25-1/28)`

`-> M =5/3(1/4 -1/28)`

`-> M =5/3( 7/28 -1/28)`

`-> M =5/3 . 6/28`

`-> M =5/14`
Vậy `M =5/14`