20. To apply the root test to an infinite series Σ an the value of n P = lim (an)¹/n 818 has to be determined. Compute p for the series 3 tan n Σ(¹)" (3 8 n=1 n C C O C C P 2. P 3. p 4. P 5. p = || = = II 4π 3 3π 16 3 100 8 3 16 4
20. To apply the root test to an infinite series Σ an the value of n P = lim (an)¹/n 818 has to be determined. Compute p for the series 3 tan n Σ(¹)" (3 8 n=1 n C C O C C P 2. P 3. p 4. P 5. p = || = = II 4π 3 3π 16 3 100 8 3 16 4
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![To apply the root test to an infinite series \(\sum a_n\), the value of
\[
\rho = \lim_{n \to \infty} (a_n)^{1/n}
\]
has to be determined. Compute \(\rho\) for the series
\[
\sum_{n=1}^{\infty} \left( \frac{3 \tan^{-1} n}{8} \right)^n
\]
Options for \(\rho\):
1. \(\rho = \frac{4\pi}{3}\)
2. \(\rho = \frac{3\pi}{16}\)
3. \(\rho = \frac{3}{8}\)
4. \(\rho = \frac{3}{16}\)
5. \(\rho = \frac{4}{3}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4a40cee-b6e7-4175-94ff-7eded3f3eb47%2F6ce9b56a-2ecb-4fdb-be3a-16d75fc7b118%2Fwwkoj1l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To apply the root test to an infinite series \(\sum a_n\), the value of
\[
\rho = \lim_{n \to \infty} (a_n)^{1/n}
\]
has to be determined. Compute \(\rho\) for the series
\[
\sum_{n=1}^{\infty} \left( \frac{3 \tan^{-1} n}{8} \right)^n
\]
Options for \(\rho\):
1. \(\rho = \frac{4\pi}{3}\)
2. \(\rho = \frac{3\pi}{16}\)
3. \(\rho = \frac{3}{8}\)
4. \(\rho = \frac{3}{16}\)
5. \(\rho = \frac{4}{3}\)
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