Problem

Determine whether the sequence converges or diver…

01:38

Problem 29 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = e^{-1/ \sqrt n} $

Name: determine whether the sequence converges or diverges if it converges find the limit a_n e 1 sqrt n
Uploaded: 2018-01-31
Duration: 1 min 12 s
Channel: Numerade
Description: Determine whether the sequence converges or diverges. If it converges, find the limit. $ a_n = e^{-1/ \sqrt n} $

Answer

Converges

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Discussion

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Video Transcript

once again we're looking at limit as n goes to infinity of Anne. If this limit exists and is finite in the sequence converges otherwise it's said to diverge. Since the exponential function is continuous, we're allowed to write this as e to the limit as n goes to infinity of minus one over squared of end. You're the continuous function. You can pull the limit inside of the function. So that's what we're doing here. And now this. This is something that we should know how to evaluate his in, goes to infinity, squared of and is going to go to infinity. So we're going to be looking at minus one over infinity, which is just like zero. So this turns into E to the zero r E to the minus zero, and that's just one. So this converges two, one

Gabriel R.

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Problem