Prove that $ (x+y)^n \le x^n +y^n$ with $x,y \ge 0 $ and $0 \lt n \le 1$
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
89175
Proof of $(a+b)^{n+1}$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
69921
Prove that: $(1+a_1)(1+a_2)...(1+a_n) \le 1 + S_n + (S_n)^2/2! + ... + (S_n)^n/n!$
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
45918
Inequality: $x^2+y^2+xy\ge 0$
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
117281
How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$