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