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For real numbers $a_i$ and $b_i$ ($i=1,\cdots,n$), We have the Cauchy-Schwarz Inequality: $$ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) $$
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