New posts in summation

Is it true that $\sum_{i=1}^n ( nGx_i^{G} + G^{x_i}) \ge n^2G + G^2n$, for all $x_i>0$, where $G=\prod_{j=1}^nx_j$?

inequality summation conjectures a.m.-g.m.-inequality

Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem

discrete-mathematics summation binomial-coefficients binomial-theorem

Counting two ways, $\sum \binom{n}{k} \binom{m}{n-k} = \binom{n+m}{n}$ [duplicate]

combinatorics summation binomial-coefficients

Limit of an Integral, Then taking Sum

calculus integration limits summation

Show that $||A-BC||_F^2 = ||A||_F^2+||BC||_F^2 - 2tr(C^TB^TA)$

summation trace matrix-norms

$1\cdot 3 + 2\cdot 4 + 3\cdot 5 + \cdots + n(n+2) = n(n+1)(2n+7)/6$ by mathematical induction

summation induction

A finite summation involving $2013$

summation

A problem with the Legendre/Jacobi symbols: $\sum_{n=1}^{p}\left(\frac{an+b}{p}\right)=0$ [duplicate]

number-theory summation legendre-symbol

Nested summations and their relation to binomial coefficients

combinatorics summation

$\sum_{k=0}^\infty \left[ \frac{n+2^k}{2^{k+1}} \right] = ?$ (IMO 1968)

algebra-precalculus elementary-number-theory summation contest-math

finding big omega of $n^k$ by splitting the sum (big-$O$ notation)

discrete-mathematics summation asymptotics ceiling-and-floor-functions

Meaning of$~\sum_\text{cyclic}$?

summation notation terminology

Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$ [duplicate]

calculus summation ceiling-and-floor-functions

Why is $\sum \limits_{k = 0}^{n} (-1)^{k} k\binom{n}{k} = 0$?

combinatorics summation binomial-coefficients

Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$

real-analysis summation

How to solve this series: $\sum_{k=0}^{2n+1} (-1)^kk $

calculus sequences-and-series summation

How to find the limit of series? (What should I know?)

calculus sequences-and-series limits summation geometric-progressions

Summation problem.

calculus summation geometric-series

How to get inverse of formula for sum of integers from 1 to n? [duplicate]

algebra-precalculus summation

Which is the explanation of the identity $\sum_{k=0}^n {n \choose k}k^2 = 2^{n-2}n(n+1)$?

combinatorics summation combinations