1/（1×3×5）+1/（3×5×7）+1/（5×7×9）+1/（7×9×11）+...+1/(2001×2003×2005)
=1/4*(1/1*3-1/3*5)+1/4(1/3*5-1/5*7)+...+1/4(1/2001*2003-1/2003*2005)
=1/4(1/1*3-1/3*5+1/3*5-1/5*7+...+1/2001*2003-1/2003*2005)
=1/4(1/1*3-1/2003*2005)
=1/12-1/(2003*8020)