1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做

1 = 1 - 1/2 1/(2×3) = 1/2 - 1/3 ……………………………… 1/[n(n + 1)] = 1/n - 1/(n + 1) 原式= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ……………… + 1/9 - 1/10 = 1 - 1/10 = 9/10