(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.]
(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
Problem 1RQ
Related questions
Question
![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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbea85843-c685-4611-8e57-d8b3fe40f7ea%2F5eb27be3-5ffe-4f05-a62f-b2fda3f7a523%2Fgtuf0m_processed.png&w=3840&q=75)
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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