Prove that:-

For any natural number **n**:-
\[n \geq 2(n!)^{\frac{1}{n}}-1\]

**Please post a non induction proof**

Prove that:-

For any natural number **n**:-
\[n \geq 2(n!)^{\frac{1}{n}}-1\]

**Please post a non induction proof**

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## Comments

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TopNewestThis can be re-arranged to this inequality

\({ \left( 1+\frac { 1 }{ n } \right) }^{ n }\ge 2\displaystyle\prod _{ k }^{ n }{ \frac { k }{ n } } \)

For \(n=1\), we have \(2=2\). Thereafter, the left side approaches \(e\) while the right side drops towards \(0\) – Michael Mendrin · 2 years, 10 months ago

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– Aman Sharma · 2 years, 10 months ago

Realy intresting proofLog in to reply

Take numbers 1,2,3.....n Then \(A.M \geq G.M\) – Krishna Sharma · 2 years, 10 months ago

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– Aman Sharma · 2 years, 10 months ago

I also did in the same wayLog in to reply