I'm having a lot of trouble with the induction step of the following proof. I really just don't even know how to start manipulating the inequality. Any help would be appreciated. Thanks.
Show that (n+1)^{(n-1)} ≤ n^{n} for all n>0.
I'm having a lot of trouble with the induction step of the following proof. I really just don't even know how to start manipulating the inequality. Any help would be appreciated. Thanks.
Show that (n+1)^{(n-1)} ≤ n^{n} for all n>0.
Make the statement that you assume $\displaystyle \displaystyle \begin{align*} \left( k + 1 \right) ^{k - 1} \leq k^k \end{align*}$, then using this assumption, try to show that $\displaystyle \displaystyle \begin{align*} \left( k + 2 \right) ^k \leq \left( k + 1 \right) ^{k + 1} \end{align*}$.