1/1x2+1/2x3+1/3x4+.+1/2011x2012=?QAQ看了别人的过程但是完全看不懂.
问题描述：
1/1x2+1/2x3+1/3x4+.+1/2011x2012=?
QAQ看了别人的过程但是完全看不懂.
答
1/1x2=1-1/2
1/2x3=1/2-1/3
1/3x4=1/3-1/4
+......+
1/2011x2012=1/2011-1/2012
1/1x2+1/2x3+1/3x4+......+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+......+1/2011-1/2012
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4......-1/2011+1/2011)-1/2012
=1-1/2012
=2011/2012
答
1/(1x2)+1/(2x3)+1/(3x4)+.+1/(2011x2012) 【运用：1/[n(n+1)]=1/n-1/(n+1)】=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2011-1/2012)=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012 【中间的都约掉了】...