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TIFR ECE 2012 | Question: 2

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Let $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ be complex numbers. Then
\[
\lim _{n \rightarrow \infty}\left|\sum_{i=1}^{k} \alpha_{i}^{n}\right|^{1 / n}
\]
is

  1. $0$
  2. $\infty$
  3. $\alpha_{k}$
  4. $\alpha_{1}$
  5. $\max _{j}|\alpha_{j}|$

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