Problem 0.1 determine whether the following sequences converge as n → ∞o: (1) an (2) an = (3) an = For (3), you may use the following identity: lim (1+¹)" = e≈ 2.718 (>1). n-x
Problem 0.1 determine whether the following sequences converge as n → ∞o: (1) an (2) an = (3) an = For (3), you may use the following identity: lim (1+¹)" = e≈ 2.718 (>1). n-x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 0.1**
Determine whether the following sequences converge as \( n \to \infty \):
1. \( a_n = \frac{n^3}{3^n} \)
2. \( a_n = \frac{n!}{e^n} \)
3. \( a_n = \frac{n^n}{n!} \)
For (3), you may use the following identity:
\[
\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e \approx 2.718 \ (> 1).
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Transcribed Image Text:**Problem 0.1**
Determine whether the following sequences converge as \( n \to \infty \):
1. \( a_n = \frac{n^3}{3^n} \)
2. \( a_n = \frac{n!}{e^n} \)
3. \( a_n = \frac{n^n}{n!} \)
For (3), you may use the following identity:
\[
\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e \approx 2.718 \ (> 1).
\]
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