lua 运行原理:从1~100中取十个数,使它们的倒数和等于1

来源:百度文库 编辑:中科新闻网 时间:2024/05/15 04:08:25
请高人解答

★答案应该是:

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10=1

这是因为:1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10
=(1-1/2)+(1/2-1/3)+……+(1/9-1/10)+1/10
=1-1/2+1/2-1/3+……+1/9-1/10+1/10
=1

这道题转换一下就是:
1=1/()+1/()+1/()+1/()+1/()+1/()+1/()+1/()+1/()+1/()
然后可以用分解的方法
★答案应该是:

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10=1

这是因为:1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10
=(1-1/2)+(1/2-1/3)+……+(1/9-1/10)+1/10
=1-1/2+1/2-1/3+……+1/9-1/10+1/10
=1

高手真多啊,学习一下