Question

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

Answer 1

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)