简算 1/1*2+1/2*3+1/3*4.1/98*99+1/99*100

简算 1/1*2+1/2*3+1/3*4.1/98*99+1/99*100
简算 1/1*2+1/2*3+1/3*4.1/98*99+1/99*100

简算 1/1*2+1/2*3+1/3*4.1/98*99+1/99*100
1/1*2+1/2*3+1/3*4.1/98*99+1/99*100
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
=1/1-1/100
=0.99

1/1*2+1/2*3+1/3*4....1/98*99+1/99*100
=1-1/2+1/2-1/3+1/3-1/4...........+1/98-1/99+1/99-1/100
=99/100

1/1*2+1/2*3+1/3*4....1/98*99+1/99*100
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
=1/1-1/100
=0.99
我是老师 谢谢采纳

这个是这样的，1/(n*(n+1))=1/n-1/(n1)
所以原式可化为：1/1-1/2+1/2-1/3+1/3-1/4....1/98-1/99+1/99-1/100=1/1-1/100=99/100

1/1*2+1/2*3+1/3*4....1/98*99+1/99*100=1-1/2+1/2-1/3+1/3-1/4+。。。+1/99-1/100=99/100

最简单的拆项法呀
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)=1+(-1/2+1/2)+(-1/3+1/3)+...+(-1/99+1/99)-1/100=99/100