Toronto Math Forum
MAT3342020F => MAT334Lectures & Home Assignments => Chapter 1 => Topic started by: yuxuan li 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

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.