1/2 + 1/6 + 1/12 + 1/20 + 1/30+ 1/42 + 1/56 + 1/72=(1+ 1/2+ 1/3+ 1/4+ 1/5)×(1/2+ 1/3+ 1/4+ 1/5+ 1/6)-(1+ 1/2+ 1/3+ 1/4+1/5+ 1/6)×(1/2+ 1/3+ 1/4+ 1/5)
问题描述:
1/2 + 1/6 + 1/12 + 1/20 + 1/30+ 1/42 + 1/56 + 1/72=
(1+ 1/2+ 1/3+ 1/4+ 1/5)×(1/2+ 1/3+ 1/4+ 1/5+ 1/6)-(1+ 1/2+ 1/3+ 1/4+1/5+ 1/6)×(1/2+ 1/3+ 1/4+ 1/5)
答
1/2 + 1/6 + 1/12 + 1/20 + 1/30+ 1/42 + 1/56 + 1/72=(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)=1-1/2+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=...