Newbetuts

Evaluating double sum $\sum_{k = 1}^\infty \left( \frac{(-1)^{k - 1}}{k} \sum_{n = 0}^\infty \frac{1}{k \cdot 2^n + 5}\right)$

Binomial sum of $n$ terms in closed form

Equality of sums with fractional parts of the form $\sum_{k=1}^{n}k\{\frac{mk}{n}\}$

Strange shape of the distribution of the sum of the binomial coefficients ${n\choose r^2}$over squares

Challenging identity regarding Bell polynomials

Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$

Sum of reciprocals of product of consecutive integers

Find the maximun of the sum $\sum_{k=1}^{n}(f(f(k))-f(k))$

Find formula for $\frac{1}{\sqrt 1}+ \frac{1}{\sqrt 2}+\cdots+\frac{1}{\sqrt n}$

Prove $1^2+2^2+\cdots+n^2 = {n+1\choose2}+2{n+1\choose3}$

Simplifying sum with rising and falling factorials

Help understanding this double sum in Feynman diagram cancellation rule

Proving that $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s$ converges when $\sum_{n=1}^{\infty}a_n $ converges

The pigeonhole principle - how to solve questions like that?

Finding the sum of geometric progression

New posts in summation

Evaluating $ \sum\frac{1}{1+n^2+n^4} $

Probability sum of 5 before sum of 7

Combinatorial proof of the identity $3^n=\sum_{k=0}^n \binom nk 2^k$

Euler phi function: $\sum_{n=1}^{N}\sum_{d\mid n}d\cdot\phi(d)$

Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$

Evaluating double sum $\sum_{k = 1}^\infty \left( \frac{(-1)^{k - 1}}{k} \sum_{n = 0}^\infty \frac{1}{k \cdot 2^n + 5}\right)$

Binomial sum of $n$ terms in closed form

Equality of sums with fractional parts of the form $\sum_{k=1}^{n}k\{\frac{mk}{n}\}$

Strange shape of the distribution of the sum of the binomial coefficients ${n\choose r^2}$over squares

Challenging identity regarding Bell polynomials

Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$

Sum of reciprocals of product of consecutive integers

Find the maximun of the sum $\sum_{k=1}^{n}(f(f(k))-f(k))$

Find formula for $\frac{1}{\sqrt 1}+ \frac{1}{\sqrt 2}+\cdots+\frac{1}{\sqrt n}$

Prove $1^2+2^2+\cdots+n^2 = {n+1\choose2}+2{n+1\choose3}$

Simplifying sum with rising and falling factorials

Help understanding this double sum in Feynman diagram cancellation rule

Proving that $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s$ converges when $\sum_{n=1}^{\infty}a_n $ converges

The pigeonhole principle - how to solve questions like that?

Finding the sum of geometric progression