a) `1/6+ 1/12+ 1/20+ 1/30+ 1/42 + 1/56`

`= 1/2.3 + 1/3.4 + 1/4.5 +1/5.6 + 1/6.7 +1/7.8`

`=1/2 - 1/3 +1/3 -1/4 +1/4 -1/5 +1/5 -1/6 +1/6 -1/7 +1/7 -1/8`  

`=1/2 +(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+(1/7-1/7)-1/8`

`= 1/2 +0+0+0+0+0-1/8`

`= 1/2- 1/8`

`= 4/8- 1/8`

`= 3/8`

b) `2/15 + 2/35 +2/63 +...+ 2/399`

`=2/3.5 + 2/5.7 + 2/7.9 +...+ 2/19.21`

`= 1/3.5 - 1/5.7 +1/7.9+...+1/19.21`

`= 1/3 - 1/5 +1/5 -1/7 +1/7 -1/9+... +1/19 -1/21`

`= 1/3-1/21`

`= 7/21- 1/21`

`=6/21`

`=2/7`

chúc chọc tốt

 

   $\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$

= ($\frac{1}{6}$ + $\frac{1}{12}$) + ($\frac{1}{20}$ + $\frac{1}{30}$) + ($\frac{1}{42}$ + $\frac{1}{56}$)

= ($\frac{2}{12}$ + $\frac{1}{12}$) + ($\frac{1}{20}$ + $\frac{1}{30}$) + ($\frac{1}{42}$ + $\frac{1}{56}$)

= $\frac{1}{4}$ + $\frac{1}{20}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$

= ($\frac{1}{4}$ + $\frac{1}{20}$) + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$

=  $\frac{3}{10}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$

=  ($\frac{3}{10}$ + $\frac{1}{30}$) + $\frac{1}{42}$ + $\frac{1}{56}$

=  $\frac{1}{3}$ + $\frac{1}{42}$ + $\frac{1}{56}$

=  ($\frac{1}{3}$ + $\frac{1}{42}$) + $\frac{1}{56}$

= $\frac{5}{14}$ + $\frac{1}{56}$

= $\frac{20}{56}$ + $\frac{1}{56}$

= $\frac{21}{56}$

= $\frac{3}{8}$