计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/60+···59/60

问题描述:

计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/60+···59/60

1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/60+···59/60=1/2+(1+2)/3+(1+2+3)/4.(1+2+3...+59)/60=1/2+1+(1+1/2)+2+(2+1/2)...(29+1/2)=(1+2+3...+29)*2+1/2*30=870+15=885