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Results tagged with sequences-and-series
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user 38620
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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this sequence $A_{n}$ have recursive relations?
Let $$A_{n}=\sum_{i=0}^{n-3}(-1)^{n+i-2}\dfrac{13n^2-31n-10ni+9i+i^2+16}{(3n-i-3)(3n-i-4)(2n-i-3)!\cdot i!}$$
I want find the $A_{n}$ recursive relations,such as following form
$$A_{n}=B_{n}+C_{n …
- 4,280
5
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3
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Find the maximum trigonometric polynomial coefficient $A_{k}$
I posted this question on Math Stack Exchange but did not get any answer. I am trying my luck here.
Let $n,k$ be given positive integers and $n>k$. If for all real numbers $x$ we have $$A_{1}\cos{x} …
- 4,280
7
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1
answer
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Does the limit of $x_n$, defined by $x_{n+1}=1/(m+1-nx_n)$ exist?
Let $m$ be positive integer, and consider the recursion
$$x_{n+1}=\frac{1}{m+1-nx_n}.$$
Does the limit of $x_n$ exist?
I'm guessing the limit doesn't exists for any $m$.
- 4,280
43
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3
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Proving $\sum_{i=1}^{n}\sum_{j=1}^{n}\left\{\frac{x_{i}}{x_{j}}\right\}\le \frac{9}{14}n^2$？
For any postive integer $n$ and for any postive real numbers $x_{1},x_{2},\cdots,x_{n}$, show that
$$\sum_{i=1}^{n}\sum_{j=1}^{n}\left\{\dfrac{x_{i}}{x_{j}}\right\}\le \dfrac{9}{14}n^2$$
Let
\begin{al …
- 4,280