Show that $(n+1)^{n-1}<n^n$ using the binomial theorem
55266
Prove that $(n+1)^{n-1}<n^n$
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
142589
Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
88144
Induction Proof $n! < n^n$
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
4931
variation of the binomial theorem
80144
Prove that $x-1$ divides $x^n-1$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$