Showing $a^n + b^n \ge (a+b)^n$ for $a,b > 0$ and $0 \le n \le 1$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
39270
Showing that $e^x > 1+x$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
75329
Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
10236
Show that $a^n \mid b^n$ implies $a \mid b$