# prove it!!!!!!!!!!!!!!!

Prove that:-

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

Please post a non induction proof

Note by Aman Sharma
3 years, 9 months ago

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This 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 $$0$$

- 3 years, 9 months ago

Realy intresting proof

- 3 years, 9 months ago

Take numbers 1,2,3.....n Then $$A.M \geq G.M$$

- 3 years, 9 months ago

I also did in the same way

- 3 years, 9 months ago