Proving A Quotient Of Two Quadratic Sequences Converges

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Problem 70: (Proving A Quotient Of Two Quadratic Sequences Converges)

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

Hint: Given $\varepsilon>0$, solve the equality $|a_M-L|=\varepsilon$ to find a value $M$ you can choose to satisfy the definition of converges.

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