câu a)1/1.5+1/5.9+1/9.13+1/13.17+...+1/41.45 b) S=1/1.2.3+1/2.3.4+...+1/23.24.25 $#huy động hai anh em siêu nhân vô làm ạ!!$

`a)` $\dfrac{1}{1 . 5}$ `+` $\dfrac{1}{5 . 9}$ `+` $\dfrac{1}{9 . 13}$ `+` `............` `+`  $\dfrac{1}{41 . 45}$ 

`=` `1/4` `.` `(` $\dfrac{4}{1 . 5}$ `+` $\dfrac{4}{5 . 9}$ `+` $\dfrac{4}{9 . 13}$ `+` `............` `+`  $\dfrac{4}{41 . 45}$ `)`

`=` `1/4` `.` `(` `1` `-` `1/5` `+` `1/5` `-` `1/9`  `+` `.........` `+` `1/41` `-` `1/45` `)`

`=` `1/4` `.` `(` `1` `-` `1/45` `)`

`=` `1/4` `.` `44/45`

`=` `11/45` 

`b)` `S` `=` $\dfrac{1}{1 . 2 . 3}$ + `..........` + $\dfrac{1}{23 . 24 . 25}$

⇒ `2S` `=` $\dfrac{2}{1 . 2 . 3}$ + `..........` + $\dfrac{2}{23 . 24 . 25}$

⇒ `2S` `=` $\dfrac{1}{1 . 2 }$ - $\dfrac{1}{2 . 3}$ + `..........` + $\dfrac{1}{23 . 24}$ - $\dfrac{1}{24 . 25}$

⇒ `2S` `=` `1` - `1/2` + `1/2` - `1/3` + .......... + `1/23` - `1/24` + `1/24` - `1/25`

⇒ `2S` `=` $\dfrac{1}{ 1. 2 }$ - $\dfrac{1}{ 24. 25 }$

⇒ `2S` `=` `299/600` 

⇒ `S` = `299/1200` 

`Vậy` `S` = `299/1200`