Inequality regarding sum of rational powers of positive real numbers
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
59624
Showing inequality for harmonic series.
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
99453
Sum of $k$-th powers
31977
How to prove sum of powers property of roots of unity?
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
123757
Proving a summation inequality with induction
103947
Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$
62417
Prove This Inequality ${\pi \over 2} \le \sum_{n=0}^{\infty} {1 \over {1+n^2}} \le {\pi \over 2} + 1$
96217
If a and b are non-negative real numbers then demonstrate inequality
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
99820
symetric inequality for a rational function of three variables
26606
Prove the inequality $\,\frac{1}{\sqrt{1}+ \sqrt{3}} +\frac{1}{\sqrt{5}+ \sqrt{7} }+\ldots+\frac{1}{\sqrt{9997}+\sqrt{9999}}\gt 24$
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$