# Questions tagged [sequences-and-series]

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.

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### On the first sequence without triple in arithmetic progression

**27**

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### Does this infinite primes snake-product converge?

**27**

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### How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k}{k(2k-1)\binom{4k}{2k}\binom{2k}k}$?

**21**

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### Is A276175 integer-only?

**20**

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### Representations of $\zeta(3)$ as continued fractions involving cubic polynomials

**16**

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### Does every real function have this weak derivation property?

**16**

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### Division of a square and value of a disk

**16**

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### How to explain the picturesque patterns in François Brunault's matrix?

**16**

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### Regularizing the divergent sum $1^k + 2^k + \cdots$

**11**

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### Does any real function have a Lipschitzian restriction on $D$?

**10**

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### About certain infinite products with the property $f(a)=f(1/a)$

**10**

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### Is there a proof that OEIS-A002387 is $[ e^{n-\gamma} ]$?

**9**

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### On the first sequence without collinear triple

**9**

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### If the generating function summation and zeta regularized sum of a divergent exist, do they always coincide?

**9**

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### Can an infinite sum depending on the logarithms of all positive integers be rational or algebraic?

**8**

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### Generalizing Ramanujan's and the Chudnovskys' 1/pi formula (Part 1)

**8**

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### The condition on $\alpha$ that $\alpha^n$ is convergent modulo 1

**8**

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### Infinite series identities in search of a proof

**8**

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### Evaluating $\sum_{k=1}^{\infty} \binom{2z}{z-kn}$

**8**

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### Is this 2x2 determinant sequence positive and increasing?

**8**

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### On the sum of consecutive primes and product of first and last

**7**

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### “Taylor series” is to “Volterra series” as “Padé approximant” is to _________?

**7**

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### Minimum length of sequence such that every integer from 1 to n can be achieved as the sum of some contiguous subsequence

**7**

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### How to prove the identity $\sum_{k=1}^\infty\frac{3H_{k-1}^2+4H_{k-1}/k}{k^2\binom{2k}k}=\frac{\pi^4}{360}$?

**7**

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### Alternative approaches to Zudilin's proof of Apéry's theorem

**7**

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### Has this self-similar sequence the ratio $(\sqrt2+1)^2$?

**7**

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### Why does a polynomial with discriminant $d=-163$ appear in this sequence?

**7**

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### in search of intepretations and connections for $k$-central binomials

**7**

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### An integral for the tribonacci constant and the general case

**7**

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### Analytic expression for the Tsirelson bound of the I3322 inequality?

**7**

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### Asymptotic behavior of a sequence of functions

**7**

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### How to assess the influence of a specific term in this telescoping series for $\zeta(s)$?

**7**

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### About the first decimal of $\sqrt {n!}$

**7**

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### Are these identities Newton series?

**7**

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### Graphs with graphic imbalance sequences

**7**

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### Composition of two formal series

**6**

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### Convergence of $\sum_{n=1}^\infty x_n^k$

**6**

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### On a certain $(-1)$-Eulerian polynomials of type $B$

**6**

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### Closed form for 2D lattice sum

**6**

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### a question about Tsirelson's space

**6**

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### Irrationality of the sum of the reciprocal of perfect powers

**6**

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### Number of Configurations in the optimal Hanoi tower

**5**

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### On rational Ramanujan-type series for $1/\pi$

**5**

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### Is there a practical application of natural integral or differintegral?

**5**

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### Counterexamples or reasonings about the transcendence of series involving the Möbius function, and polynomials in the denominator

**5**

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### Extension of Valdivia-Vogt isomorphism from $\mathscr{D}(K)$ to $\mathscr{E}'(K)$

**5**

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### A relation concerning the “sum of squares” counting function $r_2(n)$

**5**

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### A problem of Erdős on convergence of $\sum (-1)^nn/p_n$ and equidistribution of $\pi(n)$ modulo 2

**5**

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### Telescoping series for $\zeta(s)$, question about the basic ideas and a specific series

**5**

**1**answer