1+5+5^2+5^3+…+5^2004=(5^2005-1)/4应用如下公式：x^n-1=(x-1)[x^(n-1)+x^(n-2)+…+x^2+1]于是5^2005-1=(5-1)(5^2004+5^2003+…+5^2+5+1),故1+5+5^2+5^3+…+5^2004=(5^2005-1)/4.