New posts in summation

Interchange finite and infinite sum

sequences-and-series summation

Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$

combinatorics summation combinations binomial-coefficients

How to prove that $ \sum\limits_{n=1}^{\infty}n\prod\limits_{k=1}^{n}\frac{1}{1+ka} = \frac{1}{a} $?

sequences-and-series summation

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

summation permutations contest-math geometric-inequalities

Sum $\sum_{i=k}^n 3$

sequences-and-series summation

Tauber's theorem (Abel summable $\implies$ convergent) for $\sum c_n$ where $\lim_{n\to\infty} nc_n = 0$

real-analysis convergence-divergence summation fourier-analysis

How find this sum $\sum_{ab+cd=2^m}ac=?$

number-theory summation

Proof of Nesbitt's Inequality: $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$?

reference-request inequality summation infinity

computing $A_2=\sum_{k=1}^{n}\frac{1}{(z_k-1)^2} $ and $\sum_{k=1}^n \cot^2\left( \frac{k\pi}{n+1}\right)$

complex-analysis algebra-precalculus complex-numbers summation roots

Sum Involving Bernoulli Numbers : $\sum_{r=1}^n \binom{2n}{2r-1}\frac{B_{2r}}{r}=\frac{2n-1}{2n+1}$

real-analysis summation bernoulli-numbers

limit of the sum $\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n} $ [duplicate]

limits summation

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

summation binomial-coefficients factorial combinatorial-proofs

How to get ${n \choose 0}^2+{n \choose 1}^2+{n \choose 2}^2+\cdots+{n \choose n}^2 = {x \choose y}$

combinatorics binomial-coefficients summation

Proof that $\sum_{1}^{\infty} \frac{1}{n^2} <2$

calculus real-analysis summation

Collatz Conjecture: Properties of odd integers that make up a cycle

summation solution-verification collatz-conjecture

Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$

combinatorics algebra-precalculus summation binomial-coefficients

Is this series diverging? If not, what's the sum?

sequences-and-series summation divergent-series

Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$

combinatorics summation induction binomial-coefficients

If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$ [duplicate]

algebra-precalculus trigonometry summation problem-solving alternative-proof

Summation of a term to infinity

calculus sequences-and-series limits summation