New posts in Sequences And Series

Proof that any number is equal to $1$

Showing that $a$, $b$, $c$, $d$ are in geometric progression iff $(a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2$

Is the radius of convergence related to the ratio limit or half of the interval of convergence?

Why is $ \frac{5}{64}((161+72\sqrt{5})^{-n}+(161+72\sqrt{5})^{n}-2)$ always a perfect square?

$\cos\theta\cos2\theta\cos3\theta + \cos2\theta\cos3\theta\cos4\theta + ...$

$\lim_{n \to \infty} x_n = 0$ and $\lim_{n \to \infty} f(x_n) = a$

limit of the sequence $x_{n}:= \sqrt[n]{n \sqrt[n]{n \sqrt[n]{n\ldots}}}$

Problem with Summation of series

Proving $\sum_{n=0}^\infty\frac{(-1)^n\Gamma(2n+a+1)}{\Gamma(2n+2)}=2^{-a/2}\Gamma(a)\sin(\frac{\pi}{4}a)$

Does parity matter for $\lim_{n\to \infty}\left(\ln 2 -\left(-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots -\frac{(-1)^n}{n}\right)\right)^n =\sqrt{e}$?