Question

Prove by induction that $x^n-y^n$ is divisble by $x-y$ for $ n \ge 1 $

score 2.7k · Answer 1 · 2026-03-27 01:47:56

2.7k

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Prove by induction that $x^n-y^n$ is divisble by $x-y$ for $ n \ge 1 $

Published on 27 Mar 2026 - 1:47

score 27 · Answer 2 · 2026-03-25 01:16:43

27

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Verification of Green's Theorem in a Simple Case

Published on 25 Mar 2026 - 1:16

score 84 · Answer 3 · 2026-03-26 09:39:51

84

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$\lim _{A \rightarrow \infty} \int_{-A}^{A} \frac{\sin(\lambda t)}{t}e^{itx}\,dt$

Published on 26 Mar 2026 - 9:39

score 44 · Answer 4 · 2026-04-01 01:14:35

44

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Proof Verification: Suppose $X$ is a metric space and $S\subseteq X$. Then $\partial (\partial S)\subseteq \partial S$

Published on 01 Apr 2026 - 1:14

score 84 · Answer 5 · 2026-03-26 11:17:27

84

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Show that $\binom{2n}{n}\geq2^n$ for all $n\in\mathbb{N}_0$.

Published on 26 Mar 2026 - 11:17

score 76 · Answer 6 · 2026-04-02 06:24:34

76

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Find the MGF for $X\sim {\Gamma}(a,\lambda)$.

Published on 02 Apr 2026 - 6:24

score 243 · Answer 7 · 2026-03-25 11:20:19

243

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Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

Published on 25 Mar 2026 - 11:20

score 114 · Answer 8 · 2018-05-19 19:12:24

114

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$\sum_{j=1}^n\langle x_j,y_j\rangle \leq \sqrt{ \sum_{j=1}^n\langle x_j,x_j\rangle} \sqrt{\sum_{j=1}^n \langle y_j,y_j\rangle}$

Published on 19 May 2018 - 19:12

score 60 · Answer 9 · 2026-03-25 08:09:42

60

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For all $A, B \in \mathcal{M}_n(\mathbb{C})$, if $[A, [A, B]] = 0$, then $[A, B]$ is nilpotent

Published on 25 Mar 2026 - 8:09

score 507 · Answer 10 · 2026-02-23 01:23:48

507

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If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

Published on 23 Feb 2026 - 1:23

score 536 · Answer 11 · 2018-05-19 22:30:05

536

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Proof of the associative property of addition

Published on 19 May 2018 - 22:30

score 767 · Answer 12 · 2018-05-20 03:48:31

767

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Prove that if f is differentiable on $(a, b)$ and $f'$ is increasing, then $f$ is convex on $[a, b]$

Published on 20 May 2018 - 3:48

score 213 · Answer 13 · 2018-05-20 05:15:17

213

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I need some feedback on a proof from Peano axioms that $1a=a$

Published on 20 May 2018 - 5:15

score 423 · Answer 14 · 2018-05-20 07:41:26

423

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Prob. 5, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Are these sets linear continuua?

Published on 20 May 2018 - 7:41

score 64 · Answer 15 · 2026-03-26 16:04:03

64

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Line-integral: 2-form integrated over cube

Published on 26 Mar 2026 - 16:04

List Question

Prove by induction that $x^n-y^n$ is divisble by $x-y$ for $ n \ge 1 $

Verification of Green's Theorem in a Simple Case

$\lim _{A \rightarrow \infty} \int_{-A}^{A} \frac{\sin(\lambda t)}{t}e^{itx}\,dt$

Proof Verification: Suppose $X$ is a metric space and $S\subseteq X$. Then $\partial (\partial S)\subseteq \partial S$

Show that $\binom{2n}{n}\geq2^n$ for all $n\in\mathbb{N}_0$.

Find the MGF for $X\sim {\Gamma}(a,\lambda)$.

Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

$\sum_{j=1}^n\langle x_j,y_j\rangle \leq \sqrt{ \sum_{j=1}^n\langle x_j,x_j\rangle} \sqrt{\sum_{j=1}^n \langle y_j,y_j\rangle}$

For all $A, B \in \mathcal{M}_n(\mathbb{C})$, if $[A, [A, B]] = 0$, then $[A, B]$ is nilpotent

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

Proof of the associative property of addition

Prove that if f is differentiable on $(a, b)$ and $f'$ is increasing, then $f$ is convex on $[a, b]$

I need some feedback on a proof from Peano axioms that $1a=a$

Prob. 5, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Are these sets linear continuua?

Line-integral: 2-form integrated over cube

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