New posts in summation

Evaluating $\int_0^1 \frac{\ln^m (1+x)\ln^n x}{x}\; dx$ for $m,n\in\mathbb{N}$

calculus integration definite-integrals summation

$\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$

calculus integration summation soft-question alternative-proof

Help with proving a statement based on Riemann sums?

limits summation riemann-sum

Sum of the first integer powers of $n$ up to k

calculus algebra-precalculus summation binomial-coefficients

Show all roots of $\sum_{k=0}^n 2^{k(n-k)} x^k$ are real (December 6, 2014 Putnam problem)

real-analysis polynomials summation roots

Where did I go wrong in finding the sum of $1+2k+3k^2+...+nk^{n-1}$ using Abel's formula

summation solution-verification

Proof that $\sum\limits_{i=1}^n \cos \sqrt{i}$ is unbounded.

calculus sequences-and-series summation

Sum of $\{n\sqrt{2}\}$

summation random-variables asymptotics irrational-numbers fractional-part

Sum of the inverse squares of the hypotenuse of Pythagorean triangles

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

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

calculus sequences-and-series summation closed-form

Prove $\sum_{q=\alpha}^p \binom{q}{\alpha} \binom{p}{q}\frac{(-1)^q(-q)^p}{q^\alpha}=\frac{p!}{\alpha!}.$

summation binomial-coefficients factorial

Relationship between GCD, LCM and the Riemann Zeta function

number-theory elementary-number-theory summation prime-numbers analytic-number-theory

Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction [duplicate]

calculus summation alternative-proof

How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?

combinatorics summation binomial-coefficients catalan-numbers

If $\lim_{n\to\infty}\frac{1^a+2^a+...+n^a}{(n+1)^{a-1}.((na+1)+(na+2)+...+(na+n))}=\frac{1}{60}$, Find the value of a

integration limits summation

How to calculate the asymptotic expansion of $\sum \sqrt{k}$?

calculus sequences-and-series summation radicals

Another Series $\sum\limits_{k=2}^\infty \frac{\log(k)}{k}\sin(2k \mu \pi)$

sequences-and-series summation

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor$

real-analysis sequences-and-series summation closed-form euler-mascheroni-constant

Proving $\frac{200}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(2n+1)\cosh\left(\frac{\pi}{2}(2n+1)\right)}=25$

calculus sequences-and-series partial-differential-equations summation

The inequality $\,2+\sqrt{\frac p2}\leq\sum\limits_\text{cyc}\sqrt{\frac{a^2+pbc}{b^2+c^2}}\,$ where $0\leq p\leq 2$ is: Probably true! Provably true?

algebra-precalculus inequality summation a.m.-g.m.-inequality uvw