定义新运算:a*b=b-a分之1求:(1*4)+(1*9)+(1*16)+······+(1*100)
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定义新运算:a*b=b-a分之1求:(1*4)+(1*9)+(1*16)+······+(1*100)
定义新运算:a*b=b-a分之1求:(1*4)+(1*9)+(1*16)+······+(1*100)
定义新运算:a*b=b-a分之1求:(1*4)+(1*9)+(1*16)+······+(1*100)
(1*4)+(1*9)+(1*16)+······+(1*100)
=1/(4-1)+1/(9-1)+1/(16-1)+……+1/(100-1)
=1/3+1/8+1/15+……+1/99
=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/1/8-1/10+1/9-1/11)
=1/2*(1+1/2-1/10-1/11)
=1/2*(3/2-21/110)
=1/2*144/110
=36/55
不小心看到了,虽然是很简单的小学生数学题,不过闲来无事,给你解答一下吧。
1*4=1/(2^2-1)=1/((2-1)(2+1))=1/2(1-1/3)
用同样技巧
1*9=1/2(1/2-1/4)
1*16=1/2(1/3-1/5)
...
1*100=1/2(1/9-1/11)
你会发现中间好多分数可以消去,最后只剩下几个分数运算,很快得...
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不小心看到了,虽然是很简单的小学生数学题,不过闲来无事,给你解答一下吧。
1*4=1/(2^2-1)=1/((2-1)(2+1))=1/2(1-1/3)
用同样技巧
1*9=1/2(1/2-1/4)
1*16=1/2(1/3-1/5)
...
1*100=1/2(1/9-1/11)
你会发现中间好多分数可以消去,最后只剩下几个分数运算,很快得到结果
收起