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Toronto Math Forum
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MAT334--2020F
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MAT334--Lectures & Home Assignments
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Chapter 1
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Question 3 Chapter 1.4
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Topic: Question 3 Chapter 1.4 (Read 1213 times)
yuxuan li
Jr. Member
Posts: 9
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Question 3 Chapter 1.4
«
on:
October 02, 2020, 12:18:11 AM »
Can anyone solve this question?
Find the limit of each sequence that converges; if the sequence diverges, explain why.
3. z_n = n*(i/2)^n
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Xiaoyi Du
Newbie
Posts: 3
Karma: 0
Re: Question 3 Chapter 1.4
«
Reply #1 on:
October 02, 2020, 04:37:09 PM »
|z
_{n}
| = |n(i/2)
^{n}
| \leq |n/2
^{n}
|, Because i
^{1}
= i, i
^{2}
= -1, i
^{3}
= -i, i
^{4}
= 1 ...
From MAT137, we learned that |n/2
^{n}
| goes to 0 as n goes to infinity. Thus, z
_{n}
is converge sequence.
«
Last Edit: October 02, 2020, 04:45:07 PM by Xiaoyi Du
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Toronto Math Forum
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MAT334--2020F
»
MAT334--Lectures & Home Assignments
»
Chapter 1
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Question 3 Chapter 1.4