1
$\begingroup$

Just working through some practice problems before my final in a couple of weeks and I ran into one I couldn't figure out. Thanks!

Part A:

Let $ a_n = \gamma^{s/n} $ for some $ \gamma >1 $, some $ s>0$, and all positive integeers n. Show that $\lim_{n\to \infty} a_n = 1 $

Part B:

Fix some $s>0$. Determine (with proof!)

$ \lim_{n\to \infty} {\gamma^{s/n}-1\over\gamma^{1/n}-1} $

  • 0
    When you say $\lim_{x \to \infty} a_n = 1$, do you mean $n$ instead of $x$?2012-12-08

1 Answers 1

1

Hint A: Note that $\log(a_n)=\frac sn\log(\gamma)$

Hint B: Let $x=\gamma^{1/n}$ and consider $\displaystyle\lim_{x\to1}\frac{x^s-1}{x-1}$