Newbetuts

Find the sum $ \sum\limits_{a,b=0}^ \infty \begin{vmatrix} x^{a+b} & y^{a+b} & z^{a+b}\\ x^b & y^b & z^b \\ 1 & 1 & 1 \end{vmatrix} u^a v^b. $

Value of $\sum_{n=0}^{\infty} \frac{(-1)^n}{\ln(n+2)}$

What is the general formula of the sum $\sum_{k=0}^{n}(-1)^{k} \binom{n}{k}\binom{k/2}{m}$ for $m,n\in\mathbb{N}$?

Arc Length Integral of $x^x$ from 0 to 1 in closed form.

Summation of an Infinite Series: $\sum_{n=1}^\infty \frac{4^{2n}}{n^3 \binom{2n}{n}^2} = 8\pi G-14\zeta(3)$

Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$

Series question - add or remove zeroes [duplicate]

A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Combinatorial sum identity for a choose function $\sum\limits_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ [duplicate]

Convergence or divergence of $\sum_{n=1}^{\infty}\frac{1}{n^{2-\cos n}}$

Infinite summation of recursive integral

On convergence of series of the generalized mean $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s.$

Infinite Series $\sum\limits_{n=1}^\infty\frac{\zeta(3n)}{2^{3n}}$

A logarithmic integral, generalization of a result of Shalev

Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$

Sums of rising factorial powers [duplicate]

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

New posts in summation

Is there a list of the number of sets of consecutive integers that sum to n?

Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?

$\sum x_{k}=1$ then, what is the maximal value of $\sum x_{k}^{2}\sum kx_{k} $

Find the sum $ \sum\limits_{a,b=0}^ \infty \begin{vmatrix} x^{a+b} & y^{a+b} & z^{a+b}\\ x^b & y^b & z^b \\ 1 & 1 & 1 \end{vmatrix} u^a v^b. $

Value of $\sum_{n=0}^{\infty} \frac{(-1)^n}{\ln(n+2)}$

What is the general formula of the sum $\sum_{k=0}^{n}(-1)^{k} \binom{n}{k}\binom{k/2}{m}$ for $m,n\in\mathbb{N}$?

Arc Length Integral of $x^x$ from 0 to 1 in closed form.

Summation of an Infinite Series: $\sum_{n=1}^\infty \frac{4^{2n}}{n^3 \binom{2n}{n}^2} = 8\pi G-14\zeta(3)$

Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$

Series question - add or remove zeroes [duplicate]

A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Combinatorial sum identity for a choose function $\sum\limits_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ [duplicate]

Convergence or divergence of $\sum_{n=1}^{\infty}\frac{1}{n^{2-\cos n}}$

Infinite summation of recursive integral

On convergence of series of the generalized mean $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s.$

Infinite Series $\sum\limits_{n=1}^\infty\frac{\zeta(3n)}{2^{3n}}$

A logarithmic integral, generalization of a result of Shalev

Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$

Sums of rising factorial powers [duplicate]

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$