+120 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.
+61 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)
.
