a 1 =- 1；

s 1 =- 1；

a2 = s 1 S2 = s 1(s 1+a2)

a2 = 1/2；

S2 =- 1/2；

a3 = S2 S3 = S2(S2+a3)；

a3 = 1/6；

S3 =- 1/3；

(2) Hypothesis

sn =- 1/n；

(3) check

an+ 1 = snsn+ 1 =- 1/n(- 1/n+an+ 1)；

an+ 1 = 1/n- 1/(n+ 1)；

sn+ 1 = sn+an =- 1/(n+ 1)；

The hypothesis holds.

Zhang Hairu (QQ: 504902065)