Tagged Questions
2
votes
3answers
85 views
Limit of an equation similar to the Euler's constant definition
$$ \lim_{n\to \infty} \left(2+\frac{1}{n}\right)^{n} = ? $$
I don't know even how to start this.
3
votes
2answers
138 views
Potence of Euler's Number
Show with help of the Bernoulli Inequality that
$$\lim_{n\rightarrow\infty}\left(1-\frac{1}{n^2}\right)^{n}=1$$
End with:
$$\lim_{n\rightarrow\infty}\left(1-\frac{1}{n}\right)^n=\frac{1}{e}$$
33
votes
10answers
1k views
What it the fastest/most efficient algorithm for estimating Euler's Constant $\gamma$?
What it the fastest algorithm for estimating Euler's Constant $\gamma \approx0.57721$?
Using the definition:
$$\lim_{n\rightarrow\infty} \sum_{x=1}^{n}\frac{1}{x}-\log n=\gamma$$
I finally get 2 ...
5
votes
3answers
279 views
Limit of Zeta function
I'm looking for a reference for (or an elementary proof of)
$$ \lim_{s \rightarrow 1} \left( \zeta(s) - \frac{1}{s-1} \right) = \gamma$$
Thanks for your help.
