A better way to prove this inequality – math.stackexchange.com

A better way to prove this inequality – math.stackexchange.com

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Exercise 1.1.6. (b) For positive real numbers $a_1, a_2, ... , a_n$ prove that $$(a_1+a_2+ \ldots +a_n)\Big(\frac{1}{a_1}+\frac{1}{a_2}+ \ldots +\frac{1}{a_n}\Big) \geq n^2.$$ From $AM \geq GM$: ...

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