New posts in Sequences And Series

Closed-form for $ \sum_{n=0}^{\infty} \frac{x^n}{n!}n^p, $ where $p\in\mathbb{N}$

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

When does this series $\sum_{n=0}^{\infty}\sin(n!\pi x)$ converge?

Question regarding a series that contains logarithms

Prove that $\sinh{2u}+2\sinh{4u}+3\sinh{6u}+...+n\sinh{2nu}=\frac{n\sinh{(2n+2)u-(n+1)\sinh{2nu}}}{4\sinh^2{u}}$

How do you evaluate the limit of this sequence involving n-th roots?

Nested radicals like Ramanujan's infinite radicals

To show a sequence is bounded, monotone and to find its limit

Evaluating the challenging sum $\sum _{k=1}^{\infty }\frac{H_{2k}}{k^3\:4^k}\binom{2k}{k}$.

Show that the sum of a function series is bounded