True or false Calculus sequences Let $\{s_n\}$ be a sequence in $\mathbb{R}$ and assume $c \in \mathbb{R}$. If $|s_n - c| &lt; \frac{3}{n}$ for all $n \in \mathbb{N}$, then $lim_{n \rightarrow \infty} s_n = c$. 

Is this false since $|s_n - c|$ has to be less than $\varepsilon$ for every $\varepsilon &gt; 0$? In this case, its only less than $\frac{3}{n}$.
No, actually. While the definition say "for each $\epsilon &gt; 0 \ldots$ it doesn't have to explicity be epsilon. You can choose it to be any positive number. So this statement is actually true.
No, actually. While the definition say "for each $\epsilon &gt; 0 \ldots$ it doesn't have to explicity be epsilon. You can choose it to be any positive number. So this statement is actually true.