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Results tagged with limits
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user 961461
Questions on the evaluation and properties of limits in the sense of analysis and related fields. For limits in the sense of category theory, use the tag “limits-colimits” instead.
3
votes
Accepted
Limit $\lim_{k\to\infty}\left(\sum_{r=1}^{k-1}\zeta\left(2r\right)\frac{\left(-1\right)^{r+k...
{k=N+1}^{\infty}{\frac{1}{k^2}}<\sum_{k=2}^N{\frac{\varepsilon}{2^{k-1}}}+\frac{\varepsilon}{2^N}=\varepsilon
\end{align*}
By utilizing that cauchy stuff (name forgotten) and the basic definition of limits …
- 1,260
3
votes
1
answer
31
views
Evaluation of a limit involving gamma function
Basically I try to answer this question. I am almost able to prove it straight on, but I hit a roadblock at the very last step. Namely, the limit
$$
\lim_{n\rightarrow \infty} \left( \sqrt[n+1]{\Gamma …
- 1,260
5
votes
Conjecture: $\,\lim\limits_{n\to\infty}\int_0^1 (1+|\sin{nx}|)^{-2}\mathrm dx=\frac{4}{3\pi}$
=\frac{4}{3\pi}
\end{align*}
(1) Since the integrand is bounded, Lebesgue Dominated Convergence theorem could be utilized here to drag the $d$ out.
(2) By Moore-Osgood theorem, we can interchange the limits …
- 1,260
14
votes
Accepted
What is the mean value of $|\sin x +\sin (\pi x)|$?
This is not a direct answer
$\require{AMScd}$
Funny enough, I cannot tackle the integral head on, but I do have a solution to the sum equivalent to that integral.
Let's consider following question:
Su …
- 1,260
4
votes
1
answer
75
views
A conjecture involving series with zeta function
\zeta \left( N-n \right)}=\sin\left(1\right)
$$
But I believe this can applied to a broader case of limits. …
- 1,260