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Results tagged with sequences-and-series
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user 16537
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
2
votes
Accepted
Sum of subsequence, over index set of non-zero density, of monotone divergent sum also diver...
Summary. The answer to your question is "No". But it is "Yes" under the additional condition that $\liminf_n n x_n > 0$. All of this follows from work of T. Šalát in the 1960s. You find some details b …
- 10.5k
10
votes
1
answer
548
views
Who was/were the first to note that if $\sum_{x \in X} \frac{1}{x} < \infty$ then the natura...
It is a result of folklore that the natural density of a set $X$ of positive integers such that $\sum_{x \in X} \frac{1}{x} < \infty$ is zero. This is reproved, e.g., in T. Šalát's paper: Convergence …
- 10.5k