1/2 +2*1/3 +3*1/4+……+99*1/100
=(1-1/2)+(1-1/3)+(1-1/4)+……+(1-1/100)
=1*99-(1/2+1/3+1/4+……+1/100)
=99-(1/2+1/3+1/4+……+1/100)
貌似无法化简
天！你的题目意思是1/2＋1/(2×3)＋1/(3×4)＋............1/(99×100)吧?＝（1-1/2）+（1/2-1/3）+（1/3-1/4）＋............（1/99-1/100）＝1-1/100＝99/100
