Author Topic: Question 3 Chapter 1.4  (Read 339 times)

yuxuan li

  • Jr. Member
  • **
  • Posts: 9
  • Karma: 0
    • View Profile
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

Xiaoyi Du

  • Newbie
  • *
  • Posts: 3
  • Karma: 0
    • View Profile
Re: Question 3 Chapter 1.4
« Reply #1 on: October 02, 2020, 04:37:09 PM »
|zn| = |n(i/2)n| \leq  |n/2n|, Because i1 = i, i2 = -1, i3 = -i, i4 = 1 ...

From MAT137, we learned that |n/2n| goes to 0 as n goes to infinity. Thus, zn is converge sequence.
« Last Edit: October 02, 2020, 04:45:07 PM by Xiaoyi Du »