$ \dfrac{1}{7} + \dfrac{1}{91} + \dfrac{1}{247} + \dfrac{1}{475} + \dfrac{1}{775} + \dfrac{1}{1147} $

$=\dfrac{1}{1.7}  + \dfrac{1}{7.13} + \dfrac{1}{13.19} + \dfrac{1}{19.25} + \dfrac{1}{25.31} + \dfrac{1}{31.37} $

$= \dfrac{1}{6} ( 1 - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{13} + ... + \dfrac{1}{31} - \dfrac{1}{37} )$

$= \dfrac{1}{6} ( 1 - \dfrac{1}{37} )$

$= \dfrac{1}{6}  . \dfrac{36}{37} $

$= \dfrac{36}{222} = \dfrac{18}{111} = \dfrac{6}{37} $ 

Vậy $ \dfrac{1}{7} + \dfrac{1}{91} + \dfrac{1}{247} + \dfrac{1}{475} + \dfrac{1}{775} + \dfrac{1}{1147}  = \dfrac{6}{37} $

Đáp án + Giải thích các bước giải:

   `1/7+1/91+1/247+1/475+1/775+1/1147`

` = 1/1.7 + 1/7.13 + 1/13.19 + 1/19.25 + 1/25.31 + 1/31.37`

` = 1/6 . (1/1 - 1/7 + 1/7 - 1/13 +  1/13 - 1/19 + 1/19 - 1/25 + 1/25 - 1/31  + 1/31 - 1/37 ) `

`= 1/6 . ( 1 - 1/37 )`

` = 1/6 .   36/37`

` = 6/37`