Tính nhanh tổng sau A=1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80

Đặt $\frac{1}{3}$ + $\frac{1}{8}$ + $\frac{1}{15}$+ $\frac{1}{24}$+ $\frac{1}{35}$ + $\frac{1}{48}$ + $\frac{1}{63}$ + $\frac{1}{80}$ = B

=> 2B = $\frac{2}{3}$ + $\frac{2}{8}$ + $\frac{2}{15}$+ $\frac{2}{24}$+ $\frac{2}{35}$ + $\frac{2}{48}$ + $\frac{2}{63}$ + $\frac{2}{80}$

 = $\frac{2}{1*3}$ + $\frac{2}{2*4}$ + $\frac{2}{3*5}$+ $\frac{2}{4*6}$+ $\frac{2}{5*7}$ + $\frac{2}{6*8}$ + $\frac{2}{7*9}$ + $\frac{2}{8*10}$

= 1 - $\frac{1}{3}$ + $\frac{1}{2}$ - $\frac{1}{4}$ + $\frac{1}{3}$ - $\frac{1}{5}$ + $\frac{1}{4}$ - $\frac{1}{6}$ + $\frac{1}{5}$ - $\frac{1}{7}$+ $\frac{1}{6}$ - $\frac{1}{8}$ + $\frac{1}{7}$ - $\frac{1}{9}$ + $\frac{1}{8}$ - $\frac{1}{10}$

= 1 + $\frac{1}{2}$ - $\frac{1}{9}$ - $\frac{1}{10}$

= $\frac{3}{2}$ - $\frac{1}{9}$- $\frac{1}{10}$

= $\frac{25}{18}$ -$\frac{1}{10}$

= $\frac{58}{45}$

=> B = $\frac{29}{45}$