Prove that $|a+b|^r\leq 2^{r-1}(|a|^r+|b|^r)$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
56315
Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
8207
Can I prove this inequality algebraically?
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
55266
Prove that $(n+1)^{n-1}<n^n$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
81618
Prove $||a|-|b| | \leq |a-b|$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
150565
Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$