Question

Elementary proof for the sum of the numerators of the linear rational function terms of a partial fraction decomposition

score 131 · Answer 1 · 2026-03-26 07:51:44

131

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Elementary proof for the sum of the numerators of the linear rational function terms of a partial fraction decomposition

Published on 26 Mar 2026 - 7:51

score 101 · Answer 2 · 2019-09-15 19:49:49

101

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Polynomial expansion of a linear transformation (alternative proof)

Published on 15 Sep 2019 - 19:49

score 274 · Answer 3 · 2026-03-25 18:24:45

274

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Visualize Itô differentiation rule

Published on 25 Mar 2026 - 18:24

score 367 · Answer 4 · 2026-03-26 19:18:44

367

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Alternative Proof of Liouville's Theorem of Linear Flow

Published on 26 Mar 2026 - 19:18

score 73 · Answer 5 · 2026-03-25 09:50:17

73

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Inequality : $\sum_{cyc}\Big(\frac{x^4}{8x^3+5y^3}\Big)^3\geq \frac{x^3+y^3+z^3}{13^3}$

Published on 25 Mar 2026 - 9:50

score 171 · Answer 6 · 2026-03-26 23:11:36

171

Views

Prove if $a\mid b+c$ and $\gcd(b, c)=1$ then $\gcd(a, b)=1$

Published on 26 Mar 2026 - 23:11

score 1.4k · Answer 7 · 2026-03-25 21:54:07

1.4k

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find all entire functions $f$ such that $f(\frac{1}{n})=f(\frac{1}{n²})$

Published on 25 Mar 2026 - 21:54

score 123 · Answer 8 · 2026-03-25 03:22:11

123

Views

Given three non-negative numbers $x,y,z$ so that $x+y+z=100$ and $x,y,z\notin (\!33,34\!)$. Prove that $xyz\leqq 33\cdot 34\cdot 33$ .

Published on 25 Mar 2026 - 3:22

score 3.4k · Answer 9 · 2026-03-26 12:35:02

3.4k

Views

"Proof" of Konig's Theorem

Published on 26 Mar 2026 - 12:35

score 2k · Answer 10 · 2019-09-24 08:22:27

2k

Views

Prove that if $S$ be a non-empty subset of a vector space $V$, the set $\operatorname{span}(S)$ is a subspace of the vector space $V$

Published on 24 Sep 2019 - 8:22

score 154 · Answer 11 · 2019-09-25 19:24:58

154

Views

Direct telescopic proof for sum of $1^2+2^2+...+n^2$

Published on 25 Sep 2019 - 19:24

score 130 · Answer 12 · 2026-03-28 22:37:54

130

Views

Nice olympiad inequality $\frac{1}{(a+b+c)}(\sum_{cyc}\frac{ab}{7a+b})\leq \frac{1}{8}$

Published on 28 Mar 2026 - 22:37

score 210 · Answer 13 · 2019-09-26 21:20:09

210

Views

Sum of the first natural numbers: how many and what are the most common methods to verify it?

Published on 26 Sep 2019 - 21:20

score 63 · Answer 14 · 2019-09-26 22:47:29

63

Views

Let $B = \{-n +(1/n) \mid n = 2,3,4,\ldots \}$. Prove that $B$ is closed in $\mathbb R$

Published on 26 Sep 2019 - 22:47

score 1.2k · Answer 15 · 2019-09-27 22:01:53

1.2k

Views

How to prove that $n \sqrt{17}$ is irrational?

Published on 27 Sep 2019 - 22:01

List Question

Elementary proof for the sum of the numerators of the linear rational function terms of a partial fraction decomposition

Polynomial expansion of a linear transformation (alternative proof)

Visualize Itô differentiation rule

Alternative Proof of Liouville's Theorem of Linear Flow

Inequality : $\sum_{cyc}\Big(\frac{x^4}{8x^3+5y^3}\Big)^3\geq \frac{x^3+y^3+z^3}{13^3}$

Prove if $a\mid b+c$ and $\gcd(b, c)=1$ then $\gcd(a, b)=1$

find all entire functions $f$ such that $f(\frac{1}{n})=f(\frac{1}{n²})$

Given three non-negative numbers $x,y,z$ so that $x+y+z=100$ and $x,y,z\notin (\!33,34\!)$. Prove that $xyz\leqq 33\cdot 34\cdot 33$ .

"Proof" of Konig's Theorem

Prove that if $S$ be a non-empty subset of a vector space $V$, the set $\operatorname{span}(S)$ is a subspace of the vector space $V$

Direct telescopic proof for sum of $1^2+2^2+...+n^2$

Nice olympiad inequality $\frac{1}{(a+b+c)}(\sum_{cyc}\frac{ab}{7a+b})\leq \frac{1}{8}$

Sum of the first natural numbers: how many and what are the most common methods to verify it?

Let $B = \{-n +(1/n) \mid n = 2,3,4,\ldots \}$. Prove that $B$ is closed in $\mathbb R$

How to prove that $n \sqrt{17}$ is irrational?

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