What do you mean by "let"? One uses the word "let" during a definition: e.g., let w = 6. Why do you think these inequalities are true?

One way is to find an explicit formula for . It is convenient to define and so that xₙ = (aₙx₁ + bₙx₂) / 2ⁿ⁻². Then it is possible to write recurrence relations and initial conditions on aₙ and bₙ, solve them and find the limits of aₙ / 2ⁿ⁻² and bₙ / 2ⁿ⁻².