Determine whether the following sequence converges or diverges. If it converges, then find its limit. If the sequence diverges, then enter DNE In(n21) an In(10n)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
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Question
Determine whether the following sequence converges or diverges. If it converges, then find its limit. If the sequence
diverges, then enter DNE
In(n21)
an
In(10n)
Transcribed Image Text:Determine whether the following sequence converges or diverges. If it converges, then find its limit. If the sequence diverges, then enter DNE In(n21) an In(10n)
Expert Solution
Step 1

Find the sequence converges or diverges.

A sequencea,has limit L, if lim a, exist then the sequence is
converges and if it does not exist we say diverges
Step 2

Compute the sequence by taking limit on both sides,

21
In(n
In(10n)
= lim
n-o
lim
Apply power property of log in numertor
21 In(n
lim
n n10n)
It is in indeterminate form.
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