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)
.