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Let $\{a_n\}_{n \in \Bbb N} \in \Bbb R_+$ such that $$\lim_{n \to \infty} \frac{a_{n+1}}{a_n}=0 $$

Is it true that $\sup(a_n)_{n \in \Bbb N}<\infty$

Thanks for any suggestion.

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    Hint: The limit being zero means that for some $N$ you have $\frac{a_{n+1}}{a_n}<1$ for all $n>N$. – 2017-02-13
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    ok @ThomasAndrews :-) thanks i understand now – 2017-02-13

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Hint: The limit being zero means that for some $N$ you have $\frac{a_{n+1}}{a_n}<1$ for all $n>N$.