1/2*5+1/5*8+1/8*11+...+1/41*44=?

问题描述:

1/2*5+1/5*8+1/8*11+...+1/41*44=?

1/2*5=1/3*(1/2-1/5) 1/5*8=1/3*(1/5-1/8) ...1/2*5+1/5*8+1/8*11+...+1/41*44 =1/3*(1/2-1/5+1/5-1/8+1/8-1/11+...+1/41-1/44) =1/3*(1/2-1/44) =1/3*21/44 =7/44