1/2+1/(2+3)+1/(2+3+4)+...+1/(2+3+...+58)
问题描述：
1/2+1/(2+3)+1/(2+3+4)+...+1/(2+3+...+58)
答
1/2+1/(2+3)+1/(2+3+4)+.+1/(2+3+4+5+...58)
=1/2+1/[2*(2+3)/2]+1/[3*(2+4)/2]+……+1/[57*(2+58)/2]
=1/2+2/(2*5)+2/(3*6)+2/(4*7)+……+2/(57*60)
=1/2+2/3(1/2-1/5)+2/3(1/3-1/6)+2/3(1/4-1/7)+……+2/3(1/57-1/60)
=1/2+2/3(1/2-1/5+1/3-1/6+1/4-1/7+1/5-1/8+……+1/57-1/60)
=1/2+2/3(1/2+1/3+1/4-1/58-1/59-1/60)
剩下的自己算吧