(1/2+1/3+1/4+……+1/60)+(2/3+2/4+……+60/2)+(3/4+3/5+……+3/60)+……(58/59+58/60)+59/60

问题描述:

(1/2+1/3+1/4+……+1/60)+(2/3+2/4+……+60/2)+(3/4+3/5+……+3/60)+……(58/59+58/60)+59/60

原式=1/2+(1/3+2/3)+(1/4+2/4+3/4)+……+(1/60+2/60+……+58/60+59/60)
=1/2+1+(1+1/2)+……+29+(29+1/2)
=2*(1+2+……+29)+30*1/2
=2*435+15
=885