New posts in sequences-and-series

Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$

real-analysis sequences-and-series

Proof that if a complex sequence ($x_k$) converges to $a$ if and only if $a$ is an accumulation point of every subsequence of $x_k$ [duplicate]

sequences-and-series

Prob. 3, Sec. 3.4, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Does this sequence converge?

real-analysis sequences-and-series analysis limits convergence-divergence

floor number sum

sequences-and-series

On Bailey and Crandall's BBP-type sum $\sum_{n=0}^\infty \frac{1}{5^{5n}}\left(\frac{5}{5n+2}+\frac{1}{5n+3}\right)$

sequences-and-series logarithms transcendental-numbers

Proving the same sum of two subsequences by Pigeonhole Principle?

sequences-and-series combinatorics pigeonhole-principle

Does the sequence $\sin(n!\pi^2)$ converge or diverge?

sequences-and-series

On the possible values of $\sum\varepsilon_na_n$, where $\varepsilon_n=\pm1$ (i.e., changing signs of the original series)

sequences-and-series reference-request

How to prove this series $\sum_{n=1}^{\infty}\dfrac{a_{n}}{(n+1)a_{n+1}}$ diverges

sequences-and-series analysis summation

It is easy to show that $S_m=\sum_{n=1}^\infty \frac{n}{2^n + m}$ converges for any natural$\ m$, but what is its value?

calculus real-analysis sequences-and-series limits proof-writing

My proof that sum of convergent sequences converges to sum of limits

real-analysis sequences-and-series limits solution-verification

Ramanujan's sum related to $\tan^{-1}(e^{-\pi x/2})$

sequences-and-series

An upper bound for Summative Fission numbers

sequences-and-series elementary-number-theory asymptotics integers

If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

real-analysis sequences-and-series uniform-convergence

How do i evaluate this sum $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2n!}$?

real-analysis sequences-and-series summation

How to evaluate $\int_0^y\frac{\ln x\ln^2(1-x)}{x}dx$

integration sequences-and-series generating-functions closed-form harmonic-numbers

Does the series $\sum\limits_{n=2}^\infty(-1)^n\ln\left(1+\frac{\sin n}{\ln n}\right)$ converge?

sequences-and-series convergence-divergence

Is there a closed form for the alternating series of inverse harmonic numbers?

sequences-and-series harmonic-numbers

Elliptic Integrals & Gamma Functions of Rational values.

real-analysis integration sequences-and-series multivariable-calculus elliptic-integrals

Sum of $\sum_{n \geq 1} \frac{(\ln x +1)^n}{n^n}$

calculus real-analysis sequences-and-series summation power-series