x²-3x 1=0 1/1x2+1/2x3+1/3x4+.+1/2008x2009=?题中X是乘号/请详细说明所得成果/谢谢~~

1/1x2+1/2x3+1/3x4+.+1/2008x2009=?题中X是乘号/请详细说明所得成果/谢谢~~  

1/1x2+1/2x3+1/3x4+.+1/2008x2009=?题中X是乘号/请详细说明所得成果/谢谢~~

=（1/1-1/2）+（1/2-1/3）+...+(1/2008-1/2009)=2008/2009

1/1x2+1/2x3+1/3x4+.+1/2007x2008=?

1/1x2+1/2x3+1/3x4+...+1/2007x2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
中间互相抵消
=1-1/2008
=2007/2008

1+1/1x2+1/2x3+1/2x3+1/3x4+.+1/2007x2008=?

2008

1+1/1x2+1/2x3+1/3x4+.+1/2007x2008=?

1+1/1x2+1/2x3+1/3x4+...+1/2007x2008=1+(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/2007-1/2008)=2-1/2008.

1/1x2+1/2x3+1/3x4+.+1/2011x2012=？

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】
=1-1/2012
=2012/2012-1/2012
=2011/2012

1/1x2+1/2x3+1/3x4+.1/2007x2008

1/(n×(n+1))=(n+1-n)/(n×(n+1))=(n+1)/(n×(n+1))-n/(n×(n+1))=1/n-1/(n+1)
所以
1/1x2=1/1-1/2
1/2x3= 1/2-1/3
1/3x4= 1/3-1/4
……
1/2006×2007=1/2006-1/2007
1/2007×2008= 1/2007-1/2008
全部加起来
只剩下 1-1/2008=2007/2008
最终结果为2007/2008

1/1X2+1/2X3+1/3X4+.+1/2010X2011=( ) 1/1X2+1/2X3+1/3X4+.+1/n(n+1)=( ) 这两题怎么做呀~~~~

解：
1/1X2+1/2X3+1/3X4+....+1/2010X2011
=(1-1/2)+(1/2-1/3)+................+(1/2010-1/2011)
=1-1/2011
=2010/2011
1/1X2+1/2X3+1/3X4+....+1/[n（n+1）]
=(1-1/2)+(1/2-1/3)+................+[(1/n-1/(n+1)]
=1-1/(n+1)
=n/(n+1)
类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]
例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
....................
等等
这个式子是很有用的
以上希望对你有所帮助~

1/1x2+1/2x3+1/3x4+.+1/2003x2004等于多少

1/1x2+1/2x3+1/3x4+......+1/2003x2004
=1-1/2+1/2-1/3+1/3-1/4+......+1/2003-1/2004
=1-1/2004
=2003/2004

1/1x2+1/2x3+1/3x4+.+1/2011x2012=多少

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+~~~~~~+1/2005X2006

1/1x2+1/2X3+1/3X4+~~~~~~+1/2005X2006
=1-1/2+1/2-1/3+1/3-1/4++~~~~~~+1/2005-1/2006
=1-1/2006
=2005/2006