a3=a1+2d=6,s3=3a1+(3*2/2)d=12
可解出a1=2,d=2
所以sn=a1n+[n(n-1)/2]d=2n+[n(n-1)/2]d=n(n+1)
所以所求式子=1/(1*2)+1/(2*3)+...+1/n(n+1)
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)