Questions tagged [infinite-sequences]
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7 questions
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Magic square on an infinite lattice
This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with ...
- 39.9k
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References for the result that $\sqrt{n}$ is equidistributed mod 1
It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.
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Asymptotic rate for $\sum\binom{n}k^{-1}$
This MO question prompted me to ask:
What is the second order asymptotic growth/decay rate for the sum
$$\sum_{k=0}^n\frac1{\binom{n}k}$$
as $n\rightarrow\infty$?
- 43.1k
3
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Is there a summation method where the divergent series $S = U_0+U_1+U_2+\dots$ converges to a finite value?
Consider the function
$$
M(v) = \frac{m_0}{\sqrt{1 - \left(\frac{v}{c}\right)^2}},
$$ where $v \in \left]-c;c\right[$, $m_0\in\mathbb{R}^{*+}$, and $c=3\cdot10^8$.
Let $(U_n)$ be a sequence with ...
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Is there a two-dimensional Higman's lemma?
A string over a finite alphabet $A$ can be thought of as a function
$f:\{1,2,...,m\} \rightarrow A$ for some natural number $m$.
A 2-Dim string over $A$ is a function $f$ where
$f:\{1,2,\ldots,m\}\...
3
votes
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answer
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"Approximating" linear recursion with homogenous polynomial coefficients by linear recursion with constant coefficients
In a lecture I once attended, I remember the speaker using a result of the following nature:
$``$Let $\{A_n\}_{n=1}^\infty \subset \mathbb R$ be a sequence satisfying a recursion of the form
$$P(n) ...
- 739
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A second attempt at a two-dimensional Higman's Lemma
Let $A$ be a fixed finite alphabet.
If $s$ and $t$ are finite strings over $A$, define $s\leq t$ if $s$ can be obtained by deleting zero or more characters from $t$. Higman's Lemma states that if $s_1,...