New posts in summation

Find the $\frac mn$ if $T=\sin 5°+\sin10°+\sin 15°+\cdots+\sin175°=\tan \frac mn$

algebra-precalculus trigonometry summation contest-math

Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

summation induction binomial-coefficients

Proving $\sum_{x=0}^{n-1} \cos\left(k +x{2\pi\over n}\right) =\sum_{x=0}^{n-1} \sin\left(k +x{2\pi\over n}\right) =0. $

linear-algebra trigonometry summation

Root of unity filter

combinatorics complex-numbers summation binomial-theorem roots-of-unity

Summation simplification $\sum_{k=0}^{n} \binom{2n}{k}^2$

binomial-coefficients summation

Does $ \lim_{n \to \infty}\sum_{k = 1}^n \zeta\Big(k - \frac{1}{n}\Big)$ equal the Euler-Mascheroni constant?

number-theory limits summation analytic-number-theory riemann-zeta

Other variation of Nicomachus's Theorem?

summation

Double sum identity

calculus real-analysis summation

How to prove ${}_{2}F_{1}\left(\frac{1}{3},\frac{2}{3};\frac{3}{2}; \frac{27}{4}z^2(1-z)\right) = \frac{1}{z}$

integration sequences-and-series number-theory summation hypergeometric-function

Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$

combinatorics summation binomial-coefficients

Is the sum of all natural numbers $-\frac{1}{12}$? [duplicate]

sequences-and-series limits summation

Sum of first n natural numbers proof

algebra-precalculus summation arithmetic-progressions

Closed form of $\sum\limits_{i=1}^n\left\lfloor\frac{n}{i}\right\rfloor^2$?

summation closed-form ceiling-and-floor-functions

Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$

algebra-precalculus summation

Alternating sum of binomial coefficients multiplied by (1/k+1) [duplicate]

combinatorics summation binomial-coefficients

Calculate the sum of the digits of the first 100 numbers of that sequence which are divisible by 202.​

sequences-and-series elementary-number-theory summation

Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.

combinatorics summation binomial-coefficients

What is the sum of the reciprocal of all of the factors of a number?

sequences-and-series number-theory summation recreational-mathematics factoring

Prove that $1 + \frac{2}{3!} + \frac{3}{5!} + \frac{4}{7!} + \dotsb = \frac{e}{2}$

sequences-and-series trigonometry summation

Infinite geometric sum (asking for insight on an easier solution)

sequences-and-series summation contest-math generating-functions