Question

Parallelogram Inequality

score 196 · Answer 1 · 2026-03-31 18:38:15

196

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Parallelogram Inequality

Published on 31 Mar 2026 - 18:38

score 531 · Answer 2 · 2026-02-23 04:41:56

531

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If $ABC$ is a right angled triangle at $C$ then prove that $a^n+b^n<c^n$ for all $n>2$

Published on 23 Feb 2026 - 4:41

score 120 · Answer 3 · 2026-02-23 04:43:03

120

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Why does $\left|\frac{\sin(n+1)}{2^{n+1}}+...+\frac{\sin(n+p)}{2^{n+p}}\right|\leq\frac{|\sin(n+1)|}{2^{n+1}}+...+\frac{|\sin(n+p)|}{2^{n+p}}$ hold?

Published on 23 Feb 2026 - 4:43

score 91 · Answer 4 · 2026-02-23 04:43:03

91

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If $\int_a^b f(x)dx=\left[F(x)\right]_a^b$, Is $\int_a^b \lvert f(x)\rvert dx= \left[\lvert F(x)\rvert \right]_a^b$ true?

Published on 23 Feb 2026 - 4:43

score 194 · Answer 5 · 2026-02-23 04:42:57

194

Views

Proving $\sqrt{x^2-xz+z^2} + \sqrt{y^2-yz+z^2} \geq \sqrt{x^2+xy+y^2}$ algebraically

Published on 23 Feb 2026 - 4:42

score 281 · Answer 6 · 2026-02-23 04:41:53

281

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in the triangle ABC on the AC side, points M and N are chosen such that ABM = MBN = NBC

Published on 23 Feb 2026 - 4:41

score 209 · Answer 7 · 2026-02-23 04:43:04

209

Views

How to prove that if $x>0$ and $y>0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$, using the relation of arithmetic and geometric means?

Published on 23 Feb 2026 - 4:43

score 100 · Answer 8 · 2026-02-23 04:42:57

100

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$|x-a| < \epsilon$ , $|y-a| < \epsilon$ (where $x,y,a\in\mathbb R $ and $\epsilon>0$). Use the Triangle Inequality to find an estimate for $|x-y|$

Published on 23 Feb 2026 - 4:42

score 117 · Answer 9 · 2026-02-23 04:41:38

117

Views

On Resolving a Fuss on Squares and Fractions over a few Inequalities

Published on 23 Feb 2026 - 4:41

score 338 · Answer 10 · 2026-02-23 04:41:42

338

Views

how to check triangle inequality in definition of norm

Published on 23 Feb 2026 - 4:41

score 73 · Answer 11 · 2026-02-23 04:43:03

73

Views

What Inequality holds true if and only if when $|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|$ is true?

Published on 23 Feb 2026 - 4:43

score 231 · Answer 12 · 2026-02-23 04:42:57

231

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Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Published on 23 Feb 2026 - 4:42

score 66 · Answer 13 · 2026-04-01 14:58:53

66

Views

Finding modulus of a complex number

Published on 01 Apr 2026 - 14:58

score 55 · Answer 14 · 2026-02-23 04:43:04

55

Views

L1 norm of (L1 normalized vector minus original vector) less than or equal to 1 minus the L1 norm of the original vector

Published on 23 Feb 2026 - 4:43

score 190 · Answer 15 · 2026-04-01 09:45:23

190

Views

Equality case in metric spaces

Published on 01 Apr 2026 - 9:45

List Question

Parallelogram Inequality

If $ABC$ is a right angled triangle at $C$ then prove that $a^n+b^n<c^n$ for all $n>2$

Why does $\left|\frac{\sin(n+1)}{2^{n+1}}+...+\frac{\sin(n+p)}{2^{n+p}}\right|\leq\frac{|\sin(n+1)|}{2^{n+1}}+...+\frac{|\sin(n+p)|}{2^{n+p}}$ hold?

If $\int_a^b f(x)dx=\left[F(x)\right]_a^b$, Is $\int_a^b \lvert f(x)\rvert dx= \left[\lvert F(x)\rvert \right]_a^b$ true?

Proving $\sqrt{x^2-xz+z^2} + \sqrt{y^2-yz+z^2} \geq \sqrt{x^2+xy+y^2}$ algebraically

in the triangle ABC on the AC side, points M and N are chosen such that ABM = MBN = NBC

How to prove that if $x>0$ and $y>0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$, using the relation of arithmetic and geometric means?

$|x-a| < \epsilon$ , $|y-a| < \epsilon$ (where $x,y,a\in\mathbb R $ and $\epsilon>0$). Use the Triangle Inequality to find an estimate for $|x-y|$

On Resolving a Fuss on Squares and Fractions over a few Inequalities

how to check triangle inequality in definition of norm

What Inequality holds true if and only if when $|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|$ is true?

Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

Finding modulus of a complex number

L1 norm of (L1 normalized vector minus original vector) less than or equal to 1 minus the L1 norm of the original vector

Equality case in metric spaces

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