先看规律5/n(n+3)=5/3*(1/n-1/n+3)
也就是说5/(2*5)=5/3*(1/2-1/5) 5/(5*8)=5/3*(1/2-1/5) .
这样 5/(2*5)+5/(5*8)+5/(8*11)+5/(11*14)+5/(14*17)+5/(17*21)=5/3*(1/2-1/5+1/5-1/8+...+1/17-1/21)=5/3*(1/2-1/21)=5/3*19/42=95/126