Proving A Quotient Of Two Linear Sequences Converges

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Problem 67: (Proving A Quotient Of Two Linear Sequences Converges)

Prove that $\left(\frac{2n+1}{3n+4}\right)$ converges to $\frac{2}{3}$.

Hint: Given $\varepsilon>0$, solve the equality $|a_M-L|=\varepsilon$ for $M$, which should help you find a value $M$ you can choose to satisfy the definition of converges. So start by solving $\left|\frac{2M+1}{3M+4} - \frac{2}{3}\right|=\varepsilon$ for $M$.

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