∵1=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8+1/9)+(1/9-1/10) +1/10=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10
∴倒数和为1的100以内的10个不同的自然数为2,6,12,20,30,42,56,72,90,10.