Question

1/1*2+1/2*3+1/3*4+........+1/98*99+1/99*100 这个算式怎样算

Answer 1

1/1*2=1-1/21/2*3=1/2-1/3以此类推原式=1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100=1-1/100=99/100

Answer 2

1*1/2=1-1/2
1/2*1/3=1/2-1/3
1/3*1/4=1/3-1/4

.....
1/99*1/100=1/99-1/100

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 + ......+ 1/99-1/100
=1-1/100
=99/100