Complex Analysis: Theory and Applications · Problem 4.1.1

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · complex-sequence-limits

Problem

Find the following limits. (a)

\displaystyle\lim_{n\to\infty}\left(\frac{1}{2}+\frac{i}{4}\right)^n

. (b)

\displaystyle\lim_{n\to\infty}\frac{n+(i)^n}{n}

. (c)

\displaystyle\lim_{n\to\infty}\frac{n^2+i2^n}{2^n}

. (d)

\displaystyle\lim_{n\to\infty}\frac{(n+i)(1+ni)}{n^2}