Let $x_1,x_2..x_n$ be real numbers in $[-1,1]$ with $\sum_{i=1}^{n} {x_i}^3=0$ then find maximum value of :$A=\sum_{i=1}^n x_1$
107395
If the sum of $n$ cubes is zero, then the sum must be no larger than $\frac n3$.
87907
How to find the maximum and minimum value of $\left|(z_1-z_2)^2 + (z_2-z_3)^2 + (z_3-z_1)^2\right|$ (where $|z_1|=|z_2|=|z_3|=1$)?
2678
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
40635
Finding Maximum value of consecutive positive integers with constraints
128440
If $X_1,\ldots,X_n\sim Uniform(0,1)$ and $Y=\max[X_1,\ldots,X_n]$, find $E(Y)$
84990
Value of $x=\sum\limits_{n=1}^\infty {\frac{1}{10^n-1}} $ and location of second digit $1$ of $x$
16967
Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$
72360
Find the value of $a^{2m}+a^m+{1\over a^m}+{1\over a^{2m}}$
99930
Find the Maximum value of $\frac{x}{\sqrt{x+y}}+\frac{y}{\sqrt{y+z}}+\frac{z}{\sqrt{z+x}}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
106552
Find the sum of $\sum \frac{1}{k^2 - a^2}$ when $0<a<1$
124135
A general formula for $\sum (k-1)(k-2)(k-3)$?
20055
Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
137027
Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
47706
Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
91496
If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$