Prove that if $x_n$ goes to x, then $(x_1x_2\ldots x_n)^{\frac{1}{n}}$ goes to $x$.
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I've edited your question. Please take a look at it so that you could learn how to use LaTeX for next time. – Ahmad Bazzi Sep 03 '18 at 19:57
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Is it a limit? Do you mean to prove that when n goes to infinity? – Anastassis Kapetanakis Sep 03 '18 at 20:00