Inequalities 4

Algebra Level 4

If \(a_1,a_2,\cdots,a_{37}>0\)

\[\large\left(\sum\limits_{i=1}^{37}a_i\right)\large\left(\sum\limits_{i=1}^{37}\dfrac{1}{a_i}\right) \ge K\]

Find \(K\).

\(\)

Bonus:

  1. Try with power mean inequality
  2. For \(\displaystyle \left(\sum_{i=1}^n a_i\right)\left(\sum_{i=1}^n \dfrac{1}{a_i}\right) \ge X\), find \(X\).

For more inequality problems try my set.

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