先找规律,再填数1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30...则1/2011+1/2012- =1/2011*2012
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![先找规律,再填数1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30...则1/2011+1/2012- =1/2011*2012](/uploads/image/z/109033-25-3.jpg?t=%E5%85%88%E6%89%BE%E8%A7%84%E5%BE%8B%2C%E5%86%8D%E5%A1%AB%E6%95%B01%2F1%2B1%2F2-1%3D1%2F2%2C1%2F3%2B1%2F4-1%2F2%3D1%2F12%2C1%2F5%2B1%2F6-1%2F3%3D1%2F30...%E5%88%991%2F2011%2B1%2F2012-+%3D1%2F2011%2A2012)
先找规律,再填数1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30...则1/2011+1/2012- =1/2011*2012
先找规律,再填数1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30...
则1/2011+1/2012- =1/2011*2012
先找规律,再填数1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30...则1/2011+1/2012- =1/2011*2012
1/2009
1/1006
1/1+1/2-1=1/2
1/3+1/4-1/2=1/12
1/5+1/6-1/3=1/30
减去的数的分母是以1为首项1为等差的等差数列
n=(2011-1)/2+1=1006
an=1+(1006-1)=1006
所以,填1/1006
1/2011+1/2012-1/1006=1/2011*2012
很简单:在1/3+1/4-1/2=1/12中,1/2=(1/3+1/4)-1/12
在1/5+1/6-1/3=1/30中,1/3=(1/5+1/6-1/30
所以1/2011+1/2012-1/2011*2012
=(2012+2011)/2011*2012-1/2011*2012
=(2012+2011-1)/2011*2012
=4022/2011*2012=1/1006
应该填1/1006
其通项规律为:
1/(2n-1) + 1/2n - 1/n = 1/(2n-1)x 2n ,n = 1,2,3,4,5,……………………
从 1/2011 + 1/2012 - = 1/ 2011x2012 得知:
2n = 2012
故 : n = 1006
应该填: 1/1006