New posts in Sequences And Series

Evaluating $\sum _{k=1}^{\infty }\frac{H_k}{4^k\left(2k+1\right)}\binom{2k}{k}$.

Behaviour of $u_{n}=u_{\lfloor n/2\rfloor}+u_{\lfloor n/3\rfloor}+u_{\lfloor n/6\rfloor}$

Wronskian of functions $\sin(nx), n=1,2,...,k$.

Prove that $\left(1-\frac{1}{2}\right)\left(1+\frac{1}{4}\right)\left(1-\frac{1}{8}\right)\dots$ is convergent

Show that this sequence converges to $0$

Proving inequality: $\sum_{i=1}^n \left(a_i^7+a_i^5\right) \geq 2(\sum_{i=1}^n a_i^3)^2$

Starting with $1,9,9,3$ the sequence continues as the last digit of the sum of preceding 4 terms. Will subsequence $7, 3, 6, 7$ ever appear in it?

Proving the limiting behavior of functions containing iterated trigonometric functions.

summing this binomial series

The relation between uniform integrability and dominated convergence theorem in the case of counting measure