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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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Approximate sequence of numbers

Let $n \in \mathbb N$ and $k_n \in \left\{0,..,n \right\}$ then we define the numbers $$x_{n,k_n} = \frac{k_n+n^2}{n^3+n^2}.$$ It is easy to see that these numbers satisfy $$x_{n,0} = \frac{1}{n+1} …