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Results tagged with sequences-and-series
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user 8435
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.
10
votes
Nonexistence of boundary between convergent and divergent series?
As Dylan Wilson pointed out, the following question appears in Folland's real analysis book:
(second edition, pg. 164) (33) There is no slowest rate of decay of the terms of an absolutely convergent …
- 3,699
3
votes
0
answers
153
views
The behavior of series involving special subsets of the prime numbers
It is well known that the series $\sum_{p\in \mathbb{P}} \frac{1}{p}$ diverges where $\mathbb{P}$ denotes the set of primes. Brun proved that $\sum_{p\in \mathbb{P_2}} \frac{1}{p}$ converges where $ …
- 3,699
7
votes
0
answers
1k
views
A problem of Erdős on convergence of $\sum (-1)^nn/p_n$ and equidistribution of $\pi(n)$ mod...
Erdős asked1 whether the series
$$\sum_{n=1}^\infty \frac{(-1)^n n}{p_n}$$ converges.
Here, $p_n$ denotes the n-th prime.
I can show that this series converges simultaneously with the series $\sum_{ …
- 3,699