1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=
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1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=1
1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=
1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=
1/1*2+1/2*3+1/3*4+1/4*5.1/99*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+...+1/98-1/99+1/99-1/100
=1-1/100
=99/100