1.a+1/a=2 两边平方 a^2+1/a^2=2 猜想a^n+1/a^n=2
证明：a+1/a=2 因为a不等于0
所以 a*a+1=2a 得a=1
所以 a^n+1/a^n(n是任意一个自然数）等于2
2.1/[(a-n)(a-n+1)]=1/(a-n+1)-1/(a-n)
所以1/(a-1)+1/(a-1)(a-2)+1/(a-2)(a-3)+...+1/(a-2004)(a-2005)
=1/(a-1)+1/(a-2)-1/(a-1)+1/(a-3)-1/(a-2)+...+1/(a-2005)-1/(a-2004)
=1/(a-2005)
=-1/2004