1/n(n+1)=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012
1/1x2+1/2x3+1/3x4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/n(n+1)=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012
1/1x2+1/2x3+1/3x4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)