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Question: you are given that a sequence xn converges to x...

Question details

You are given that a sequence (xn) converges to x ∈ R. It is also given that (xn) satisfies the recursive equation

x_n+1 = αx_n + β ∀n ∈ N,

where α, β ∈ R are independent of n and α 6= 1.

Use relevant theorems to find the value of x.

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