I have to prove the following $\frac{2n² - 5}{3n²+7n} = 2/3$ .... How do I solve it for n? Right now I'm stuck at $\frac{15+14n}{3(3n²+7n)}$$ < \epsilon$ Note : My problem is that I don't understand how to isolate n
2026-04-09 05:25:26.1775712326
Doubt in an example of sequence using $\varepsilon$
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You don't need to isolate $n$ in that expression. You can note that $$ \dfrac{15+14n}{3n^2+7n}\leq \dfrac{15n}{3n^2} = \frac 5n $$
and then argue that $$ \frac 5n < \varepsilon \Rightarrow \dfrac{15+14n}{3n^2+7n} < \varepsilon. $$