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This question already has an answer here:

Let's assume that $a_{1},a_{2},...,a_{n}$ are positive. How to prove this inequality:

$(a_{1}+a_{2}+...+a_{n})(\frac{1}{a_{1}}+\frac{1}{a_{2}}+...+\frac{1}{a_{n}})\geq n^{2}$

My effort: I don't know where to begin.

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merged by Alexander Gruber Jan 28 at 6:24

This question was merged with Proof that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$ because it is an exact duplicate of that question.

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