There is the positive real roots of a family of polynomials of the form: p(n) = x^n - x^(n-1) - ... - x - 1; n ≥ 1. Let r(n) be the smallest positive real root of p(n). Find two real numbers a and b with the property that a ≤ r(n) ≤ b for all n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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There is the positive real roots of a family of polynomials of the form:

p(n) = x^n - x^(n-1) - ... - x - 1; n ≥ 1.

Let r(n) be the smallest positive real root of p(n). Find two real numbers a and b with the property that a ≤ r(n) ≤ b for all n

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