1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值是?还有没了呢?

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1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值是?还有没了呢?

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值是?还有没了呢?
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值是?
还有没了呢?

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值是?还有没了呢?
如果a=1,b=2
原式=(1/1-1/2)+(1/2-1/3)+.(1/2008-1/2009)
=1-1/2009
=2008/2009