New posts in sequences-and-series

$\sum_{i=1}^{89} \sin^{2n} (\frac{\pi}{180}i)$ is a dyadic rational

sequences-and-series trigonometry

How to prove this conjecture $x_{n}(n\ge 4)$ can't be an integer.

sequences-and-series number-theory

Strange approximation to $\sqrt{\pi}$

sequences-and-series approximation radicals irrational-numbers pi

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Computing a limit of a sum mixed with product.

real-analysis sequences-and-series algebra-precalculus limits infinite-product

Many convergent sequences imply the initial sequence zero?

sequences-and-series divergent-series

If $\lim\limits_{n \to \infty} a_n$ exists is it true that $a_n$ is bounded?

calculus sequences-and-series limits limits-without-lhopital

A trigonometric series

sequences-and-series

Summation of divergent series of Euler: $0!-1!+2!-3!+\cdots$

real-analysis sequences-and-series approximation divergent-series

Help me prove this inequality :

sequences-and-series inequality summation

How to prove that $\sum_{n=1}^{\infty}\frac{1!+2!+\cdots+n!}{(2n)!}$ converges?

sequences-and-series convergence-divergence

Convergence of $\sum\limits_{n=1}^{\infty}{{n!n^{-p}}\over{q(q+1)...(q+n)}}$

real-analysis calculus sequences-and-series

What exactly is a Collatz-like Problem

sequences-and-series number-theory dynamical-systems collatz-conjecture

Proving a series of a subsequence converges

real-analysis sequences-and-series convergence-divergence

Sum of $1+\frac{1}{2}+\frac{1\cdot2}{2\cdot5}+\frac{1\cdot 2\cdot 3}{2\cdot 5\cdot 8}+\cdots$

sequences-and-series summation

Proving $\zeta(2) - \beta(1) + \zeta(4) - \beta(3) + \zeta(6)- \beta(5) + \ldots=1$

sequences-and-series special-functions riemann-zeta zeta-functions

Asymptotic behaviour of $\sum_{p\leq x} \frac{1}{p^2}$

sequences-and-series number-theory asymptotics analytic-number-theory

Why is this sum equal to $0$?

sequences-and-series analysis summation products

Closed form to an interesting series: $\sum_{n=1}^\infty \frac{1}{1+n^3}$

calculus integration sequences-and-series closed-form digamma-function

Integral $\int_0^1(x(1-x))^n\frac{d^n}{d^n x}(\log x \cdot\log (1-x))dx$

calculus integration sequences-and-series definite-integrals