Tag: sequences-and-series
- Prove that $\displaystyle\lim _{n \rightarrow \infty} n a_n=0$
- Bijection between Cantor set and binary sequences; Hunter
- Approximate Maclaurin series for $\sqrt x$
- Prove that $\sum_{n\geq 1}(\sqrt[n]{n}-1)$ diverges.
- Taylor expansion of $\frac{\operatorname{arctanh}(x)}{1+x^2}$
- A question on Beta function
- Sum involving Triangular Numbers
- Let $\{a_n\}$ satisfy $a_1=1, a_{n+1}=\sin(a_n)$, find $\lim_{n\to\infty}\frac{\log(a_n)}{\log(n)}$.
- Compute $\lim_{n \to \infty}\prod_{k=1}^n (\frac{k}{n})^{1/n}$
- Prove that $(1+\frac{1}{n})^{n+\frac{1}{2}}>e$ for all positive integer $n$