Recursion of S_n=x_1^n + x_2^n + x_3^n

Makena Preston

Makena Preston

Answered question

2022-07-17

Recursion of S n = x 1 n + x 2 n + x 3 n

Answer & Explanation

Reinfarktq6

Reinfarktq6

Beginner2022-07-18Added 18 answers

x 1 , x 2 , x 3 are roots of P ( x ) = x 3 α x 2 + β x γ
Then, plugging in x i and multiplying by x i n you get
x i n + 3 α x i n + 2 + β x i n + 1 γ x i n = 0 .
Adding the three relations we get the relation Thomas Andrews wrote:
S n + 3 α S n + 2 + β S n + 1 γ S n = 0 .

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