化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1

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化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分

化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1
化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1

化简:x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
.
1/(x+2006)(x+2007)=1/(x+2006)-1/(x+2007)
x(x+1)分之1+(x+1)(x+2)分之1+(x+2)(x+3)分之1+.+(x+2006)(x+2007)分之1
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+2006)-1/(x+2007)
=1/x-1/(x+2007)
=2007/x(x+2007)

原式=
1/x-1/(1+X)+1/(1+x)-1/(x+2)……-1/(x+2006)+1/(x+2006)-1/(x+2007)
=1/x-1/(x+2007)

原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+....+1/(x+2006)-1/(x+2007)
=1/x-1/(x+2007)

2005