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Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

 Jun 12, 2025
 #4
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Something that might help: 

Cauchy-Schwarz inequality states that

(∑aibi)2≤(∑ai2)(∑bi2)open paren sum of a sub i b sub i close paren squared is less than or equal to open paren sum of a sub i squared close paren open paren sum of b sub i squared close paren

(𝑎𝑖𝑏𝑖)2≤(𝑎2𝑖)(𝑏2𝑖)

.

 Jun 18, 2025

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