S2=a^2+b^2=(a+b)^2-2ab=3
S3=a^3+b^3=(a+b)^3-3ab(a+b)=4
s4=a^4+b^4=(a^2+b^2)^2-2(ab)^2=7
2. Because (a+b)*Sn- 1
=a^n+b^n+ab^(n- 1)+ba^(n- 1)
=Sn+ab*Sn-2
Use Sn- 1=Sn-Sn-2 instead of a+b= 1, ab=- 1,
That is Sn=Sn- 1+Sn-2.
3.S7=S6+S5
=S5+S4+S4+S3
=S4+S3+S4+S3
=2*(4+7)
=22