1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+2006)(x+2007)过程

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1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+2006)(x+2007)过程
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+2006)(x+2007)过程

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+2006)(x+2007)过程
解: 1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+2006)(x+2007)
=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)
=[(x+2007)-x]/x(x+2007)
=2007/x(x+2007)
注: 这里只需记住公式1/x(x+1)=1/x-1/(x+1)
一般地: 1/ab=(b-a)(1/a-1/b)

x+xxXXXXX+x+Xx+CXXxVDDF+x+x+xxxx+xx+=xXXx(Xx=xX+Xx=XXXX)=XXXXXXX

=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)
=2007/x(x+2007)

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