Đáp án+Giải thích các bước giải:

`1/6 -1/35-1/63-1/99-1/143-1/195`

`=1/6 - 1/2(2/35+2/63+2/99+2/143+2/195)`

`=1/6 - 1/2(2/(5.7)+2/(7.9)+2/(9.11)+2/(11/13)+2/(13.15))`

`=1/6 - 1/2(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)`

`=1/6  - 1/2(1/5-1/15)`

`=1/6 -  1/2 . 2/15`

`=1/6 - 1/15`

`=1/10`

Đáp án:

`1/10`

Giải thích các bước giải:

`1/6-1/35-1/63-1/99-1/143-1/195`

$=$`1/6+(-1)/35+(-1)/63+(-1)/99+(-1)/143+(-1)/195`

$=\dfrac16+(-1).\left(\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac1{195}\right)\\=\dfrac16+(-1).\left(\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}+\dfrac1{13.15}\right)\\=\dfrac16+\dfrac{-1}{2}\cdot\left(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}+\dfrac2{13.15}\right)\\=\dfrac16+\dfrac{-1}{2}\cdot\left(\dfrac15-\dfrac17+\dfrac17-\dfrac19+\dfrac19-\dfrac1{11}+\dfrac1{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac1{15}\right)\\=\dfrac16+\dfrac{-1}{2}\cdot\left(\dfrac15-\dfrac{1}{15}\right)\\=\dfrac16+\dfrac{-1}{2}\cdot\dfrac{2}{15}\\=\dfrac16+\dfrac{-1}{15}\\=\dfrac{1}{10}$