(n) Q(n) Show that, if P(x) and Q(x) are polynomials of positive degrees, then the sequence an = converges to 1. [Hint: First show that the n’th root of the absolute value of any non-zero polynomial in n converges to 1, by applying the Squeeze Theorem and the fact that limn→∞ √√/n : = 1 = limn→∞ WC, for any constant c > 0.]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that, if P(x) and Q(x) are polynomials of positive degrees, then the sequence an
converges to 1.
=
n
VIE
P(n)
Q(n)
[Hint: First show that the n'th root of the absolute value of any non-zero polynomial in n converges
to 1, by applying the Squeeze Theorem and the fact that limɲ→∞ √√/n = 1 = limn→∞ √c, for any
constant c> 0.]
Transcribed Image Text:Show that, if P(x) and Q(x) are polynomials of positive degrees, then the sequence an converges to 1. = n VIE P(n) Q(n) [Hint: First show that the n'th root of the absolute value of any non-zero polynomial in n converges to 1, by applying the Squeeze Theorem and the fact that limɲ→∞ √√/n = 1 = limn→∞ √c, for any constant c> 0.]
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