New posts in sequences-and-series

Part 1: Does the arithmetic mean of sides right triangles to the mean of their hypotenuse converge?

real-analysis sequences-and-series geometry number-theory summation

Computing $\int \sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\cdots}}}} \,\mathrm{d}x$

sequences-and-series definite-integrals

What is the value of $\sin 1 ^\circ \sin3^\circ\sin5^\circ \sin 7^\circ \sin 9^\circ \cdots \sin 179^\circ $?

sequences-and-series trigonometry

Relationship between rate of convergence and order of convergence

sequences-and-series analysis numerical-methods

Convergence of a sequence $c_n$

calculus sequences-and-series limits convergence-divergence

Concerning the classical normalized Eisenstein series

sequences-and-series reference-request modular-forms

Does the series $\sum \sin^{(n)}(1)$ converge, where $\sin^{(n)}$ denotes the $n$-fold composition of $\sin$?

calculus sequences-and-series trigonometry convergence-divergence

Prove $\lim_{m\to\infty}\sum_{k=1}^m\frac{2^{-k}}{k} = \log 2$

sequences-and-series

Is there a formula for sums of consecutive powers, where the powers are non integer?

sequences-and-series

Sum of series $\sin x + \sin 2x + \sin 3x + \cdots $

sequences-and-series analysis

On the Euler sum $\sum \limits_{n=1}^{\infty} \frac{H_n^{(4)} H_n^2}{n^6}$

real-analysis sequences-and-series complex-analysis

$\frac{dS}{d\rho}$ Factor arising

real-analysis linear-algebra sequences-and-series ordinary-differential-equations solution-verification

Infinite sum of reciprocal shifted Fibonacci numbers

sequences-and-series convergence-divergence fibonacci-numbers

de Bruijn sequence in which order of subsquences doesn't matter

sequences-and-series combinatorics

Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$

calculus real-analysis sequences-and-series limits

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

sequences-and-series analysis continuity proof-verification uniform-continuity

A finite sum of prime reciprocals

sequences-and-series elementary-number-theory prime-numbers

On the summation $\sum \limits_{n=1}^{\infty} \arctan \left ( \frac{1}{n^3+n^2+n+1} \right )$

real-analysis sequences-and-series

An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

real-analysis calculus sequences-and-series summation harmonic-numbers

Conjecture $\sum_{n=0}^\infty a_n= \frac{1}{2}-\frac{7 \zeta(3)}{2 \pi^2}$

sequences-and-series logarithms riemann-zeta conjectures