谁能帮我解决一些数学题目啊

来源:百度知道 编辑:UC知道 时间:2024/07/18 15:34:01
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)

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
=1-1/9
=8/9

(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)
=(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)
=(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4+1/5)+(1+1/2+1/3+1/4+1/5)×1/6-(1+1/2+1/3+1/4+1/5)×(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)×1/6
=(1+1/2+1/3+1/4+1/5-1/2-1/3-1/4-1/5)×1/6
=1×1/6
=1/6

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)+....+(1/8-1/9) [然后拆括号]
=1-1/2+1/2-1/3.....+1/8-1/9
=1-1/9
=8/9

1/2 + 1/6 + 1/12 + 1/20 + 1/30+ 1/42 + 1/56 + 1/72= 8/9

(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