Triangle Inequality question with fractions
56315
Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
138490
An inequality with a weird condition
93599
General Proof for the triangle inequality
111903
An inequality for sides of a triangle
17264
Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
88605
Proof of the Reverse Triangle Inequality
104922
Inequality $\frac1a + \frac1b + \frac1c \leq \frac{a^8+b^8+c^8}{a^3b^3c^3}$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
32963
proving the inequality $\triangle\leq \frac{1}{4}\sqrt{(a+b+c)\cdot abc}$
116206
Complex number question on proving an inequality.
127866
Two triangles and their content ratio
39015
Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
98043
How to visualize Reverse Triangle Inequality $||\mathbf{a}| − |\mathbf{b}|| ≤ |\mathbf{a} − \mathbf{b}|$?
133428
How prove this inequality $\frac{a}{b+3}+\frac{b}{c+3}+\frac{c}{d+3}+\frac{d}{a+3}\le 1$
91662
Proof for triangle inequality for vectors
95116
Frobenius Norm Triangle Inequality