化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.

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化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.
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化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.
化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.

化简求值:1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006),其中X=1.
1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006)
=1/x-1/(x+1)+1/(x+1)-1/(x+1)+...+1/(x+2005)-1/(x+2006)
=1-1/(x+2006)
=(x+2005)/(x+2006)
当x=1时
原式=2006/2007


1/x(x+1)+1/(x+)(x+2)+.....1/(x+2005)(x+2006）
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+2004)-1/(x+2005)+1/(x+2005)-1/(x+2006)
=1/x-1/(x+2006)
=[(x+2006)-x]/x(x+2006)
=2006/[x(x+2006)]=2006/(2006+1)=2006/2007

=(1/x -1/(x+1) ) + (1/(x+1) -1/(x+2) ) + ....+( 1/(x+2005) -1/(x+2006) )
=1/x -1/(x+2006)
=1-1/2007
=2006/2007

原式=1/x-1/（x+1）+1/(x+1)-1/(x+2)+...+1/(x+2005)-1/(x+2006)
=1/x-1/(x+2006)
=1-1/2007
=2006/2007

题目错了，后面1/(x+)(x+2)+.....中没数值

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