一、1/(2*2-1)+1/(4*4-1)+1/(6*6-1)+.+1/(100*100-1)
=1/(2+1)(2-1)+1/(4+1)(4-1)+...+1/(100+1)(100-1)
=(1/2)(1/(2-1)-1/(2+1)+1/(4-1)-1/(4+1)+...+1/(100-1)-1/(100+1))
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=50/101;
二、【1-1/（2*2）】*【1-1/(3*3）】*【1-1/(4*4）】*.*【1-1/（2004*2004）】
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)*.*(1+1/2004)(1-1/2004)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)*..*(2005/2004)(2003/2004)
=(2005/2)(1/2004)
=2005/4008