How to show Triangle inequality
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If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
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Simple algebra square root inequality
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Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
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How to show the given equality
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Frobenius Norm Triangle Inequality
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Inequality plot with PGFPlots
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How can I prove this inequality for $n\geq 2$?
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Using the triangle inequalities to prove a bound in the complex plane
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Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
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Reverse Triangle Inequality in vector space
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Inequality involving sides of a triangle
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Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
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Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
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Proving inequality $|\sin(n\theta) |\le n\sin\theta$
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Graphs of Linear Inequalities
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Proving Inequalities with Absolute values
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showing certain vertices form an equilateral triangle