New posts in Limits

Show that the sequence defined as $x_{n+1}=\sqrt[3]{x_n+x_{n-1}}$ converges

$\lim_{n\to\infty} \frac{10^n}{\sqrt{(n+1)!} + \sqrt{n!}}\,.$

Given a recursion $a_{n+ 1}= \sqrt{na_{n}+ 2n+ 1}$ with $a_{1}\geq 1.$ Prove that $a_{n}\sim n\,{\rm as}\,n\rightarrow\infty$

Compute the limit of the sequence $x_n=(2-\sqrt{2})(2-\sqrt[3]{2})...(2-\sqrt[n]{2})$

What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$

Follow-up Question about Cesaro mean proof

Proving $\prod_{n=1}^{\infty}\left(1+\frac{1}{n^{3}}\right)=\frac{1}{\pi}\cosh\frac{\pi\sqrt{3}}{2}$

Right versus left derivative by increasing one-sided derivatives

Is $\lim_{x\to\infty} (0.99999...)^x=1$?

Determine : $\lim _{n \rightarrow \infty} \left[\frac{1 \cdot 1 !+2 \cdot 2 !+\cdots+n \cdot n !}{(n+1) !}\right]^{(n+1)!}$