1/(12+13)+1/(13+14)+.+1/(19+20)=

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1/(12+13)+1/(13+14)+.+1/(19+20)=1/(12+13)+1/(13+14)+.+1/(19+20)=1/(12+13)+1/(13+14)+.+1/(19+20)=1/(1

1/(12+13)+1/(13+14)+.+1/(19+20)=
1/(12+13)+1/(13+14)+.+1/(19+20)=

1/(12+13)+1/(13+14)+.+1/(19+20)=
1/(12+13)+1/(13+14)+.+1/(19+20)
=(1/12 - 1/13) + (1/13 - 1/14) + ...+(1/19-1/20)
=1/12-1/13+1/13-1/14+1/14-1/15……-1/20
=1/12-1/20
=5/60-3/60
=2/60
=1/30

原式 = (1/12 - 1/13) + (1/13 - 1/14) + ... +(1/19-1/20)
= 1/12 - 1/20
= 1/30

楼上两位...是加号不是乘号啊....