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