One line proof of CS inequality

I don’t think I have seen shorter proof of Cauchy-Schwarz Inequality than the following

\displaystyle\frac{\sum a_k b_k}{\sqrt{(\sum a_{k}^{2})(\sum b_{k}^{2})}}=1-\frac{1}{2}\sum\left(\frac{a_k}{\sqrt{(\sum a_{k}^2)}}-\frac{b_k}{\sqrt{(\sum b_{k}^2)}}\right)^2

which immediately gives

\displaystyle\frac{\sum a_k b_k}{\sqrt{(\sum a_{k}^{2})(\sum b_{k}^{2})}}\le 1

from which CS inequality follows.

Source: Mathematics Magazine, Vol. 68, No. 2 (Apr., 1995), p. 97

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