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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Proof that superlinearly convergent sequence converges faster than linearly convergent sequence

Given real sequences $(a_n)_{n\in\mathbb{N}}$ and $(b_n)_{n\in\mathbb{N}}$, both converging to the same limit $A$ and such that $|a_n-A|\neq 0$ and $|b_n-A|\neq 0$ for every $n$ sufficiently large, we …
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