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Junior high school with additional math problems
Lang Jun hunting English team to answer your questions ~

1)S 1= 1，S2=3，S3=4，S4=7，S5= 1 1，S6= 18。 In fact, according to the second question, you can also get a solution.

2) Direct proof is enough.

a^(n+2)+b^(n+2)=(a+b)[a^(n+ 1)+b^(n+ 1)]-ab(a^n+b^n)

That is, S[n+2]=S[n+ 1]+S[n]

3) In fact, A and B are (1+√5)/2 and (1-√5)/2, which can be verified by Vieta's theorem.

The equation to be solved is S2=3.

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