1/2*4+1/4*6+1/6*8........+1/198*200

1/2*4+1/4*6+1/6*8........+1/198*200
=(2/2*4+2/4*6+2/6*8........+2/198*200)/2
=[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+........+(1/198-1/200)]/2
=(1/2-1/200)/2
=99/400

每一项可以提取1/4

0.25(1/1*2+1/2*3+1/3*4...1/99*100)
=0.25(1-1/2+1/2-1/3+1/3-1/4+...1/99-1/100)

=0.25(1-1/100)=99/400

1/2*4+1/4*6+1/6*8........+1/198*200
=1/4*(1/1*2+1/2*3+1/3*4+......+1/99*100)
=1/4*(1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100)
=1/4*(1-1/100)=99/400

1/2*4=(1/4)*（1/1-1/2)
1/4*6=(1/4)*（1/2-1/3)
...
1/198*200=(1/4)*（1/99-1/100)

1/2*4+1/4*6+1/6*8........+1/198*200
=(1/4)*(1/1-1/2+1/2-1/3+...+1/99-1/100)
=(1/4)*(1-1/100)
=99/400

原式=1/4(1/1*2+1/2*3+......1/99*100)....其中（1/n*(n+1)=1/n-1/(n+1))
所以=1/4*(1-1/2+1/2-1/3+……+1/99-1/100）
=1/4*(1-1/100)
=1/4*99/100
=99/400