For the infinite series series n=1 n=1 1 2n it is clear that lim 1 is convergent? Why or why not? 2n n 1 = 0. Can we use this fact to conclude that the infinite 2n
For the infinite series series n=1 n=1 1 2n it is clear that lim 1 is convergent? Why or why not? 2n n 1 = 0. Can we use this fact to conclude that the infinite 2n
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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Question
![For the infinite series
\[
\sum_{n=1}^{\infty} \frac{1}{2n},
\]
it is clear that
\[
\lim_{n \to \infty} \frac{1}{2n} = 0.
\]
Can we use this fact to conclude that the infinite series
\[
\sum_{n=1}^{\infty} \frac{1}{2n}
\]
is convergent? Why or why not?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68a5d243-ead0-4e66-a982-77eeed741d35%2F507d0365-60bb-4c2c-ad39-d779466cc33c%2Fjy0df5q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For the infinite series
\[
\sum_{n=1}^{\infty} \frac{1}{2n},
\]
it is clear that
\[
\lim_{n \to \infty} \frac{1}{2n} = 0.
\]
Can we use this fact to conclude that the infinite series
\[
\sum_{n=1}^{\infty} \frac{1}{2n}
\]
is convergent? Why or why not?
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