Waste less time on Facebook — follow Brilliant.
×

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
2 years, 4 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

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 \(0\) Michael Mendrin · 2 years, 4 months ago

Log in to reply

@Michael Mendrin Realy intresting proof Aman Sharma · 2 years, 4 months ago

Log in to reply

Take numbers 1,2,3.....n Then \(A.M \geq G.M\) Krishna Sharma · 2 years, 4 months ago

Log in to reply

@Krishna Sharma I also did in the same way Aman Sharma · 2 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...