Tried the squeeze theorem but it didn't get me anywhere since:
$0 \leftarrow \frac{1}{n^{1-1/n}}=\frac{n^{1/n}}{n}\leq\frac{(1^n+2^n+...+n^n)^{1/n}}{n}\leq \ n^{1/n}\to 1$
None of the other tools we studied seem to work. Any tips? Thanks.
Tried the squeeze theorem but it didn't get me anywhere since:
$0 \leftarrow \frac{1}{n^{1-1/n}}=\frac{n^{1/n}}{n}\leq\frac{(1^n+2^n+...+n^n)^{1/n}}{n}\leq \ n^{1/n}\to 1$
None of the other tools we studied seem to work. Any tips? Thanks.
$\frac{\left(1^n+2^n+...+n^n\right)^{1/n}}{n} = \left(\left(\frac{1}{n}\right)^n+\left(\frac{2}{n}\right)^n+...+1^n\right)^{1/n} \geq (1)^{1/n} = 1 \rightarrow 1$
The rest is as you suggest.