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Ask a math problem, please have a look at it.
1.S 1=a+b= 1

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