New posts in summation

Proving that $\sum_{k=0}^n\frac{1}{n\choose k}=\frac{n+1}{2^{n+1}}\sum_{k=1}^{n+1}\frac{2^k}{k}$

combinatorics summation binomial-coefficients fractions

Reworking $\sum_{n \leq x} \frac{1}{n^s}$, where $n$ is relatively prime to some fixed $k$

number-theory summation asymptotics

If the earth's rotational speed increased by 2% each day starting today…what would be the difference in age 20 years from now?

summation

Show that $\left(\sum_{r=1}^n r\right)^2=\sum_{r=1}^n r^3$ without expanding to closed form

summation

How to prove this inequality with this $\sqrt{n\left(x_{1}^{2}+x_{2}^{2}+\dots+x_{n}^{2}\right)} $

multivariable-calculus inequality summation cauchy-schwarz-inequality

Does this double series converge?

real-analysis combinatorics sequences-and-series summation

Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$

combinatorics summation

Manipulation of inferior and superior limits of a summation

summation geometric-series

Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum

algebra-precalculus summation

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

Asymptotic behaviour of sum over the inverse japanese symbol

real-analysis summation asymptotics

Proving $\sum _{k=1}^n \frac{(-1)^{k-1} 16^k (k-1)! k! (k+n-1)!}{((2 k)!)^2 (n-k)!}=\frac{4}{n}\sum _{k=1}^n \frac{1}{2 k-1}$

integration definite-integrals summation special-functions

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

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

real-analysis discrete-mathematics summation ceiling-and-floor-functions

Find the sum: $\sum_{n=0}^\infty \frac{(n!)^2}{(2n)!}x^n$

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

Using complex analysis for evaluating summations: some general queries

sequences-and-series complex-analysis summation complex-integration

When is infinite sum bounded by an integral?

inequality integration summation

Formula for finite sum $\sum_{1\leq\alpha_{1}<\alpha_{2}<\ldots<\alpha_{k}\leq n}\frac{\alpha_{1}+\alpha_{2}+\ldots+\alpha_{k}}{k}$

combinatorics summation

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

calculus summation ceiling-and-floor-functions polylogarithm

How to evaluate the sum : $\sum_{k=1}^{n} \frac{k}{k^4+1/4}$

sequences-and-series algebra-precalculus summation telescopic-series