How to prove these binomial coefficients?

[fighter5555]

Binomial Coefficients

How do you proof that
(n/k)^k<=(n k)<=n^k/k!

 

[eblue]

Re: Binomial Coefficients

It is impossible to prove. Left side is n^k / k^k, and right side is n^k / k! , double check the source.

 

[jorgito]

Binomial Coefficients

Not too hard to prove.....
Do you still need it?

Best regards

 

[greek]

Binomial Coefficients

By taking limits

 

[v_naren]

Re: Binomial Coefficients

\[k=k\]
\[k>k-1\]
\[k>k-2\]
\[.........\]
\[k>1\]
\[=>k^k > k!\]
\[=>{\frac{1}{k^k}}<{\frac{1}{k!}}
\]
\[=> {(\frac{n}{k})}^k < \frac{n^k}{k!}\]