规律:1/n×1/(n+4)=1/4×[1/n-1/(n+4)]
1x1/5+1/5x1/9+1/9x1/13+…+1/2001x1/2005
=1/4x(1-1/5)+1/4x(1/5-1/9)+1/4x(1/9-1/13) + 1/4x(1/13-1/17) +.+1/4×(1/2001-1/2005)
=1/4×(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+.+1/2001-1/2005)
=1/4×(1-1/2005)
=1/4×2004/2005
=501/2005