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Convergence of sequences and different modes of convergence.

This tag is for questions about Convergent Sequences and Series and their existence.

Formally, a sequence $S_n$ converges to the limit $S.$

$$\lim_{n\to \infty}S_n=S $$ if, for any $\epsilon>0$, there exists an $N>0$ such that $|S_n-S|<\epsilon$ for $n>N$

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