3/5+3/45+3/117+.+3/3995997=3/(1×5)+3/(5×9)+3/(9×13)+.+3/(1197×2001)我们有：3/(n×(n+4))=3/4*(1/n-1/(n+4))所以,原式=3/4*(1/1-1/5+1/5-1/9+1/9-13+.+1/1197-1/2001)=3/4*(1-1/2001)=3/4*2000/2001=500/667...