1. 1/a(a+1) + 1/（a+1)(a+2) + 1/（a+2)(a+3) + .+1/（a+2003)(a+2004)
=1a-1/(a+1) + 1/(a+1)-1/(a+2) +1/(a+2)+.-1/(a+2003)+1/(a+2003)-1/a+2004)
=1/a-1/(a+2004)
=(a+2004-a)/{a(a+2004)
=2004/{a(a+2004)
2. 1/x - 1/x-1 （x²-1/x -x+1）
= 1/x - 1/(x-1) {(x^2-1) -x(x-1)}/x
= 1/x - 1/(x-1) {(x^2-1 -x^2 +x)}/x
= 1/x - 1/(x-1)*(x-1)/x
= 1/x - 1/x
=0
3. 1/(a+2) + ( a-2)
={1+(a+2)(a-2)}/(a+2)
={1+a^2-4)}/(a+2)
=(a^2-3)/(a+2)