Problem #WSP-5326

Problem

Prove the $H M - G M$ inequality for positive real numbers $a_{1}, a_{2}, . . . a_{n}$ : $\frac{n}{\frac{1}{a_{1}} + . . . \frac{1}{a_{n}}} \leq \sqrt[n]{a_{1} a_{2} . . . a_{n}} .$

To see the solution register and get verified.