![Photo-induced copper-catalyzed sequential 1,n-HAT enabling the formation of cyclobutanols | Nature Communications Photo-induced copper-catalyzed sequential 1,n-HAT enabling the formation of cyclobutanols | Nature Communications](https://media.springernature.com/m685/springer-static/image/art%3A10.1038%2Fs41467-021-26670-5/MediaObjects/41467_2021_26670_Fig1_HTML.png)
Photo-induced copper-catalyzed sequential 1,n-HAT enabling the formation of cyclobutanols | Nature Communications
![real analysis - If $a_{n+1}=\frac{3+a_n^2}{a_n+1}$ and $a_1=1$, then what is $\lim\limits_{n\to\infty}\left(\frac{4}{3}\right)^n(3-a_n)$? - Mathematics Stack Exchange real analysis - If $a_{n+1}=\frac{3+a_n^2}{a_n+1}$ and $a_1=1$, then what is $\lim\limits_{n\to\infty}\left(\frac{4}{3}\right)^n(3-a_n)$? - Mathematics Stack Exchange](https://i.stack.imgur.com/wj0wk.jpg)
real analysis - If $a_{n+1}=\frac{3+a_n^2}{a_n+1}$ and $a_1=1$, then what is $\lim\limits_{n\to\infty}\left(\frac{4}{3}\right)^n(3-a_n)$? - Mathematics Stack Exchange
![calculus - Determine whether the series $ \ \sum_{n=1}^{\infty} (-1^n) (1 - \frac{1}{n})^{n^2} $ converges absolutely, or converges conditionally, or diverges. - Mathematics Stack Exchange calculus - Determine whether the series $ \ \sum_{n=1}^{\infty} (-1^n) (1 - \frac{1}{n})^{n^2} $ converges absolutely, or converges conditionally, or diverges. - Mathematics Stack Exchange](https://i.stack.imgur.com/iL6nI.jpg)
calculus - Determine whether the series $ \ \sum_{n=1}^{\infty} (-1^n) (1 - \frac{1}{n})^{n^2} $ converges absolutely, or converges conditionally, or diverges. - Mathematics Stack Exchange
![algorithm - Given 1 < a < 10, 1 ≤ n ≤ 100000, show how to compute the value of 1 × a + 2 × a^2 + 3 × a^3 + . . . + n × a^n efficiently, i.e. in O(log n)! - Stack Overflow algorithm - Given 1 < a < 10, 1 ≤ n ≤ 100000, show how to compute the value of 1 × a + 2 × a^2 + 3 × a^3 + . . . + n × a^n efficiently, i.e. in O(log n)! - Stack Overflow](https://i.stack.imgur.com/JY892.png)