你的分数打错了.应该是:1/2+1/6+1/12+1/30+1/42+1/56+1/72+1/90+1/110
分析,1/2=1-1/2 1/6=1/2-1/3 1/12=1/3-1/4 ……1/110=1/10-1/11
把上面各数换成减法算式就是:
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/10-1/11(中间的数全部抵消)
=1-1/11
=10/11
你的分数打错了.应该是:1/2+1/6+1/12+1/30+1/42+1/56+1/72+1/90+1/110
分析,1/2=1-1/2 1/6=1/2-1/3 1/12=1/3-1/4 ……1/110=1/10-1/11
把上面各数换成减法算式就是:
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/10-1/11(中间的数全部抵消)
=1-1/11
=10/11