MathAnalysisCalculusLimits

Limits of sequences

The edge

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Let's consider the sequence defined by the formula $a_{n} = \frac{1}{n^{2}}$ Its limit is 0. Let's fix some $\varepsilon > 0$ . What will be the smallest $N\in\mathbb{N}$ such that $|a_n| < \varepsilon$ for all $n > N$ ?

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N = \lceil 1/\varepsilon \rceil

N = \lceil \varepsilon^{2}\rceil

N = \lceil 1/\varepsilon^{2} \rceil

N = \lceil 1/\sqrt{\varepsilon} \rceil

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