New posts in summation

Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$ [duplicate]

sequences-and-series summation recurrence-relations

Prove that sum is finite

sequences-and-series convergence-divergence special-functions summation divergent-series

Prove that $\sum_{k=0}^n{e^{ik^2}} = o(n^\alpha)$, $ \forall \alpha >0$

real-analysis summation

Does the sum converge for all values of $a$?

convergence-divergence summation

How to sum this infinite series

sequences-and-series elementary-number-theory summation

Is there a way to evaluate analytically the following infinite double sum?

real-analysis calculus sequences-and-series trigonometry summation

Binomial Coefficients Proof: $\sum_{k=0}^n {n \choose k} ^{2} = {2n \choose n}$.

combinatorics summation binomial-coefficients

Proving that $\sum_{n=1}^\infty \frac{\sin\left(n\frac{\pi}{3}\right)}{(2n+1)^2}=\frac{G}{\sqrt 3} -\frac{\pi^2}{24}$

integration summation closed-form

The Soup Problem: how to asymptotically fairly split a geometric series and a constant one using a single pattern?

sequences-and-series summation puzzle number-systems combinatorics-on-words

Summation of Central Binomial Coefficients divided by even powers of $2$

summation binomial-coefficients

A formula for the sum of the triangular numbers? [duplicate]

discrete-mathematics summation

A Ramanujan-type identity: $11\sum_{n=1}^{\infty}\frac{n^3}{e^{2n\pi}-1}-16\sum_{n=1}^{\infty}\frac{n^3}{e^{4n\pi}-1}=\frac{1}{48}$

sequences-and-series summation residue-calculus

How find this Fibonacci sequence sum $\sum_{k=0}^{\infty}\frac{1}{F_{2^k}}$

sequences-and-series summation

Closed-form for $B=\lim_{n\to\infty}\sum_{a_1=1}^{\infty}\frac{1}{a_1^2}\sum_{a_2=1}^{a_1}\frac{1}{a_2^2}\cdots\sum_{a_n=1}^{a_{n-1}}\frac{1}{a_n^2}$?

sequences-and-series limits summation recreational-mathematics

Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$

algebra-precalculus summation binomial-coefficients recreational-mathematics binomial-theorem

An inequality about the sum of distances between points : same color $\le$ different colors?

inequality summation euclidean-geometry geometric-inequalities

How to evaluate the sum $\sum_{n=1}^{\infty}\frac{1}{(2n+1)(2n+2)}\left(1+\frac{1}{2}+...+\frac{1}{n}\right)$

calculus summation harmonic-numbers

How do I find the sum of arithmetic series? [duplicate]

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

sequences-and-series summation closed-form harmonic-numbers

How to solve $\binom{n}{1}^2+2\binom{n}{2}^2 + 3\binom{n}{3}^2 + 4\binom{n}{4}^2+\cdots + n\binom{n}{n}^2$?

combinatorics summation binomial-coefficients