Question

Find if the limit, if it exists!
a. (1/n e^nπi/6)
b. (1/n e^nπ/6)
c. (Log[e^i(π +(-1)^n/n])
d. (Log[e^2nπi])

Answer 1

Assuming you want the limit as n→∞
(a) |e^ix| <= 1, so the limit is 0
(b) exponentials grow faster than polynomials, so the limit is →∞
(c) the limit is the same as log(e^iπ) = log(-1)
Or so I thought. wolframalpha.com says it's logπ + i
Hmmm.
(d) since e^2nπi oscillates between -1 and 1, the log does not converge