Question 3 Chapter 1.4

[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]

|z_n| = |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, z_n is converge sequence.