New posts in Sequences And Series

Generalizing Catalan numbers: number of ways where we cross the diagonal $k$ times.

Quadratic Euler sums $\sum _{n=1}^{\infty } \frac{(-1)^{n-1} \widetilde H(n)^3}{2 n+1}$

Closed form solution to recurrence: $g(n)=(k-2)g(n-1)+(k-1)g(n-2)$

How Can I prove $\sum_{n=1}^{\infty}{\frac{n^4}{5^n}}=\frac{285}{128}$

Find all sequences that has $\sum_{i=1}^\infty a_i$ converges, where $a_i = \sum_{k=i+1}^\infty a_k^2$.

If $\sum_{n=1}^{\infty} a_{n}$ converges, then$\sum_{n=1}^{\infty} \sin(a_{n})$ also converges

$x_{n+13}=x_{n+4}+2x_{n}$, $x_{143}=...$

Evaluate $\lim_{n\to\infty} \prod_{k=1}^n \frac{2k}{2k-1}\int_{-1}^{\infty} \frac{{\left(\cos{x}\right)}^{2n}}{2^x} \; dx$

For any sequence of real numbers, one can always find a subsequence that is monotone

Recursive sequence, $x_{1} \geq 0, x_{n+1}=\sqrt{x_{n}+2}$