New posts in sequences-and-series

Concerning this sum $\sum_{n=0}^{\infty}\frac{1}{4n+1}\left[\frac{1}{4^n}{2n \choose n}\right]^2=\frac{\Gamma^4\left(\frac{1}{4}\right)}{16\pi^2}$

sequences-and-series

Hopping to infinity along a string of digits

sequences-and-series recreational-mathematics irrational-numbers decimal-expansion turing-machines

Is every Wolstenholme number greater than or equal to its index?

sequences-and-series

An interesting binomial summation

integration sequences-and-series summation binomial-coefficients

How to prove that this sequence converges? ($a_n=a_{a_{n-1}}+a_{n-a_{n-1}}$)

sequences-and-series

Prove $\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots$ converges to $\frac 1 2 $

calculus sequences-and-series

Proving that product of two Cauchy sequences is Cauchy

real-analysis sequences-and-series cauchy-sequences

Simplifying product of differences

sequences-and-series

Insight about $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{\cos(nx)\cos(my)}{n^2+m^2}$

sequences-and-series

Find asymptotic of recurrence sequence

calculus sequences-and-series limits asymptotics recurrence-relations

Proving that $\frac{\pi ^2}{p}\neq \sum_{n=1}^{\infty }\frac{1}{a_{n}^2}$

sequences-and-series number-theory

If $a_i\geq 0,$ prove $\sum\limits_{n=1}^\infty\frac{a_1+a_2+\cdots+a_n}{n}$diverges.

sequences-and-series analysis

Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$

real-analysis sequences-and-series

Show that $(f_n)$ is equicontinuous, given uniform convergence

real-analysis sequences-and-series

Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$

calculus sequences-and-series convergence-divergence telescopic-series

About a possible Hardy-type inequality for negative exponents

sequences-and-series functional-analysis inequality integration

On the closed form for $\sum_{m=0}^\infty \prod_{n=1}^m\frac{n}{4n-1}$

sequences-and-series hypergeometric-function

How do I find the sum of a sequence whose common difference is in Arithmetic Progression?

sequences-and-series

Do the Fibonacci numbers contain any run of digits?

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

How to find the sum $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots =\ ?$

sequences-and-series convergence-divergence summation fourier-analysis fourier-series