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What is the maximum product of n positive numbers if their sum is given?
TurlapatyAnishChand
Let the sum of series a1,.., an = A. Since ai >0.
Then the maximum possible product of a1,..,an is = (A/n)n.
This result basically comes the relation between the arithmetic mean and geometric mean of n positive numbers.
A/n >= (a1...an)(1/n).
The equality case of the above relation gives the maximum product (by raising the power by n on both sides).
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