MAT334--2020F > Chapter 1

Question 3 Chapter 1.4

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yuxuan li:
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:
|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.