Divide numerator and denominator by n². Since |sin(eˣ)| ≤ 1 and 0 ≤ x⁸ ≤ 1, the quotient converges uniformly to 1/7. For example, its difference from 1/7 is bounded by 8/(49n²). Thus α = 1/7 and **14α = 2**.
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