|x-2|+|y-4|=0 Here we know that the result can be 0 only when x-2=y-4=0. That is to say, x=2 and y=4.

Have you got the wrong question?

According to symmetry, the question seems to be

1 1 1 1

——+ ————+ ———— +......+————————

xy(x+2)(y+2)(x+4)(y+4)(x+20 10)(y+20 10)

= 1 \ (2 * 4)+ 1 \ (4 * 6)+ 1 \ (6 * 8)+...+ 1 \ (20 12 * 2065438+

= ( 1 \ 2) * [ 1 \ 2- 1 \ 4+ 1 \ 4- 1 \ 6+ 1 \ 6- 1 \ 8

= (1\ 2) * [1\ 2-1\ 2014] cancel each other out.

End.

If it is the original question, it may be more troublesome. The way is similar, but the first two items are calculated separately ~ ~ ~