(1)
S1 = a+b = 1
S2 = a^2+b^2 = (a+b)^2 -2ab = 1 +2 = 3
S3 = a^3+b^3 = (a+b)(a^2-ab+b^2) =1*(S2 -ab) = 3+1 = 4
S4 = a^4+b^4 = (a^2+b^2)^2 -2a^2b^2 = (S2)^2 -2(ab)^2 =9 -2 =7
(2) Sn = Sn-2 + Sn-1
(3) 根据（1）和（2）的结果,
S5 = S4+S3 = 7+4 = 11
S6 = S5+S4 = 11+7 =18
S7 = S6+S5 = 18+11=29
即 a^7 + b^7 =29