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Suppose $a>0$. Consider the sequence $a_n = n \{ \sqrt[n]{ea} – \sqrt[n]{a}, \:\:\:\:\: n \geq 1$. Then

  1. $\underset{n \to \infty}{\lim} a_n$ does not exist
  2. $\underset{n \to \infty}{\lim} a_n=e$
  3. $\underset{n \to \infty}{\lim} a_n=0$
  4. none of the above
in Calculus by Veteran (431k points)
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