Question

Show $\frac{x}{\left(1+x^2\right)^{n}}\underset{{n\to +\infty}}{\sim} \frac{1}{x^{2n-1}}$ for every $x>1$

score 98 · Answer 1 · 2016-08-19 12:27:32

98

Views

Show $\frac{x}{\left(1+x^2\right)^{n}}\underset{{n\to +\infty}}{\sim} \frac{1}{x^{2n-1}}$ for every $x>1$

Published on 19 Aug 2016 - 12:27

score 90 · Answer 2 · 2016-08-19 14:01:54

90

Views

Prove that $f_n(x): x\in\mathbb{R}\mapsto \frac{x}{(1+x^2)^{n}}$ converges pointwise to null function

Published on 19 Aug 2016 - 14:01

score 188 · Answer 3 · 2026-04-01 02:01:53

188

Views

Need an elegant proof for $(q-r)x+(r-p)y+(p-q)z=0$ with given premises

Published on 01 Apr 2026 - 2:01

score 576 · Answer 4 · 2016-08-20 10:03:43

576

Views

Existence of an infinite group with finitely many conjugacy classes

Published on 20 Aug 2016 - 10:03

score 112 · Answer 5 · 2016-08-20 18:46:10

112

Views

A surjective morphism between two commutative finite rings induce a surjective morphism between the groups of units

Published on 20 Aug 2016 - 18:46

score 50 · Answer 6 · 2016-08-20 19:52:54

50

Views

Proof verification - working with integers

Published on 20 Aug 2016 - 19:52

score 262 · Answer 7 · 2016-08-21 22:14:48

262

Views

Proof regarding the multiplicative group of integers modulo $p^m$

Published on 21 Aug 2016 - 22:14

score 1k · Answer 8 · 2026-03-29 23:48:13

1k

Views

Symmetric group $\mathfrak{S}_4$ does not have a normal subgroup of order 2.

Published on 29 Mar 2026 - 23:48

score 145 · Answer 9 · 2016-08-22 15:52:57

145

Views

Proof that $\sum_{n=1}^{\infty}2^{-3n} = \frac{1}{7}$

Published on 22 Aug 2016 - 15:52

score 140 · Answer 10 · 2016-08-22 21:08:15

140

Views

Is there a neater proof for $\lim_{x \rightarrow 1} 1/x = 1$?

Published on 22 Aug 2016 - 21:08

score 1.1k · Answer 11 · 2026-04-01 18:47:29

1.1k

Views

The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic

Published on 01 Apr 2026 - 18:47

score 149 · Answer 12 · 2026-02-24 10:18:37

149

Views

If $u(x) = \int_1^x \sin(x-t)t^2 dt$, then $u'' + u -x^2 = 0$

Published on 24 Feb 2026 - 10:18

score 320 · Answer 13 · 2016-08-24 17:04:09

320

Views

Short proof for the determinant of a $4$ by $4$ matrix

Published on 24 Aug 2016 - 17:04

score 116 · Answer 14 · 2026-03-25 14:23:34

116

Views

alternative proof of graph property implying $3$ edge connectivity.

Published on 25 Mar 2026 - 14:23

score 227 · Answer 15 · 2016-08-27 14:13:11

227

Views

Inductive proof of kth falling power

Published on 27 Aug 2016 - 14:13

List Question

Show $\frac{x}{\left(1+x^2\right)^{n}}\underset{{n\to +\infty}}{\sim} \frac{1}{x^{2n-1}}$ for every $x>1$

Prove that $f_n(x): x\in\mathbb{R}\mapsto \frac{x}{(1+x^2)^{n}}$ converges pointwise to null function

Need an elegant proof for $(q-r)x+(r-p)y+(p-q)z=0$ with given premises

Existence of an infinite group with finitely many conjugacy classes

A surjective morphism between two commutative finite rings induce a surjective morphism between the groups of units

Proof verification - working with integers

Proof regarding the multiplicative group of integers modulo $p^m$

Symmetric group $\mathfrak{S}_4$ does not have a normal subgroup of order 2.

Proof that $\sum_{n=1}^{\infty}2^{-3n} = \frac{1}{7}$

Is there a neater proof for $\lim_{x \rightarrow 1} 1/x = 1$?

The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic

If $u(x) = \int_1^x \sin(x-t)t^2 dt$, then $u'' + u -x^2 = 0$

Short proof for the determinant of a $4$ by $4$ matrix

alternative proof of graph property implying $3$ edge connectivity.

Inductive proof of kth falling power

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