Please help with calculating limit of a sequence: $lim(n/3^n)$ , where $n$ goes to infinity.

Asked Oct 23 '19 at 10:42

Active Oct 23 '19 at 10:42

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Actually it is obvious that this limit of a sequence $lim(n/3^n)$ where $n$ goes to infinity and $n$ is a natural number equals to zero, because the function $3^n$ is growing faster that the function $n$. Yet I cannot prove it in my school just by saying that because infinity divided by infinity is an indefinite expression in limits. Normally I would try to modify the expression, but here I do not know how to do that. Could you help me please to modify the argument of this limit so that I could argue that it really equals to zero?

asked Oct 23 '19 at 10:42

TKN

Hint: since you know the terms are positive, what happens if you use the fact that $n < 2^n$ ? – Ninad Munshi Oct 23 '19 at 10:44
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Relevant: https://math.stackexchange.com/questions/1514814/unknown-limit-result-lim-n-to-infty-n-an – Matti P. Oct 23 '19 at 10:44

Please help with calculating limit of a sequence: $lim(n/3^n)$ , where $n$ goes to infinity.

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