Prove that $a^n-b^n \geq (a-b)nb^{n-1}$ where $a \geq b \geq 0$
138036
Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
54369
Proof of $n^2 \leq 2^n$.
149287
Prove that $A,B>0$ and $A_{ij}0$
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
92975
Does $a^n \mid b^n$ imply $a\mid b$?
16852
$|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
48211
When is $(a+b)^n \equiv a^n+b^n$?