已知数列{an}的前n项和为Sn,a1= - 2/3,满足Sn + 1/Sn+2=an(n>=2),计算S1,S2,S3,S4,并猜想Sn得表达式

S2+1/S2+2=a2=s2-a1=s2+2/3 s2=-3/4 s3+1/s3+2=a3=s3-s2=s3+3/4 s3=-4/5 s4+1/s4+2=a4=s4-s3=s4+4/5 s4=-5/6 sn=-(n+1)/(n+2)