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anemone
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Assume that $x_1,\,x_2,\,\cdots,\,x_n \ge -1$ and $\displaystyle \sum_{i=1}^n x_i^3=0$. Prove that $\displaystyle \sum_{i=1}^n x_i \le \dfrac{n}{3}$.
Summation is a mathematical operation that involves adding a sequence of numbers together. Inequality refers to a mathematical statement that compares two quantities, indicating which is larger or smaller.
Summation is used to find the total value of a sequence of numbers. It is commonly used in calculus, statistics, and other branches of mathematics to represent the total of a continuously changing quantity.
The symbol used for summation is the uppercase Greek letter sigma (∑). It is typically written above the sequence of numbers to be added together.
An inequality statement is a mathematical expression that compares two quantities using symbols such as <, >, ≤, or ≥. It represents a relationship between the values of the two quantities, indicating which is greater or less than the other.
Summation and inequality are related in that summation can be used to represent the total value of a sequence of numbers, while inequality can be used to compare the values of two quantities. Inequality statements can also be used to represent the upper and lower bounds of a summation.