New posts in Sequences And Series

Convergence/Divergence of Complex Series $\sum\limits_{n=1}^{\infty} \frac{n(2+i)^n}{2^n}$

Proving $\int_0^\infty\left(\frac{x^xe^{-x}}{\Gamma(x+1)}-\frac1{\sqrt{2\pi x}}\right)dx=-\frac13$

Prove $\sum_{n=0}^{\infty} \frac{\Gamma(n+(1/2))}{4^n(2n+1)\Gamma(n+1)}=\frac{\pi^{3/2}}{3}$

Justifying $\sum_{n=0}^\infty\log(1+x^{2^n}) = -\log(1-x)$ for $0\le x<1$

How to obtain the sum of the series $\sum_{n=0}^{\infty}\frac{1}{2^{n}(3n+1)}$?

How to evaluate $ \:\sum _{n=3}^{\infty \:}\frac{4n^2-1}{n!}\:\: $?

What is the motivation for sequences to be defined on natural numbers?

How to calculate the limit of sequence

What is value of this integral? $\int_{0}^{\infty}\frac{\log(1+4x^2)(1+9x^2)(9+x^2)+(9+x^2)\log(4+x^2)(10+10x^2)}{(9+x^2)^{2}(1+9x^{2})}dx$

Existence of limit for sequence $x_n=\frac12\left(x_{n-1}+\frac8{x_{n-2}}\right)$ with initial values $x_0=5,x_1=10$