A First Course in Complex Analysis · Problem 7.5.1

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · sequence-convergence-divergence

Problem

For each of the sequences, prove convergence or divergence. If the sequence converges, find the limit. (a)

a_n = e^{\frac{\pi i n}{4}}

(b)

a_n = \frac{(-1)^n}{n}

(c)

a_n = \cos(n)

(d)

a_n = 2 - \frac{i n^2}{2n^2+1}

(e)

a_n = \sin\!\left(\frac{1}{n}\right)