Prove that $2^{n-1}(a^n+b^n)\geq(a+b)^n$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
16798
Prove the inequality $n! \geq 2^n$ by induction
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
20964
Proof that $n^2 < 2^n$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
88838
How can I prove this inequality for $n\geq 2$?
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
48211
When is $(a+b)^n \equiv a^n+b^n$?
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$