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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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Sum of a terms in a divergent series taken along indices the sum of whose reciprocal diverge...

What about if (for n bigger than 2) you take x(n)=(nlog(n))^(-1) and k(n) roughly same as x(n)^(-1) (say integral part of nlog(n))? Then both conditions required are satisfied, while the subseries wa …
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