Question

Evaluate $\lim_{n\ \rightarrow\ \infty\ }\ \left(\frac{\sqrt{1\times3}+\sqrt{2\times4}+\cdots\sqrt{n\times\left(n+2\right)}}{n}-\frac{n}{2}\right)$

score 153 · Answer 1 · 2023-04-13 15:41:33

153

Views

Evaluate $\lim_{n\ \rightarrow\ \infty\ }\ \left(\frac{\sqrt{1\times3}+\sqrt{2\times4}+\cdots\sqrt{n\times\left(n+2\right)}}{n}-\frac{n}{2}\right)$

Published on 13 Apr 2023 - 15:41

score 92 · Answer 2 · 2023-04-14 13:41:33

92

Views

Infinity times minus one

Published on 14 Apr 2023 - 13:41

score 105 · Answer 3 · 2023-04-17 13:37:37

105

Views

representing $\int_0^\infty{\frac{\sin x}{x^3}}dx$ in terms of $\int_0^\infty{\frac{\sin^3x}{x^3}}dx$

Published on 17 Apr 2023 - 13:37

score 166 · Answer 4 · 2023-04-25 22:38:00

166

Views

Why are the improper integrals $\int_{-\infty}^{\infty}x\,\mathrm{d}x$ and $\lim\limits_{n\to\infty} \int_{-n}^{n}x\,\mathrm{d}x$ different?

Published on 25 Apr 2023 - 22:38

score 35 · Answer 5 · 2023-05-02 07:00:28

35

Views

For infinite sets A,B do we also have $A\subseteq B\rightarrow|A|\leq|B|$?

Published on 02 May 2023 - 7:00

score 210 · Answer 6 · 2023-05-03 03:11:59

210

Views

What is the cardinality of the set of injective functions from $\mathbb{N}$ to $\mathcal P \mathbb{N}$?

Published on 03 May 2023 - 3:11

score 26 · Answer 7 · 2026-03-26 21:12:22

26

Views

Does this beginningless-past thought experiment result in several possible non-well-ordered sets?

Published on 26 Mar 2026 - 21:12

score 110 · Answer 8 · 2023-05-07 10:53:10

110

Views

What is truly infinity?

Published on 07 May 2023 - 10:53

score 844 · Answer 9 · 2023-05-13 14:59:28

844

Views

Does a recursive definition of a variable make sense at all?

Published on 13 May 2023 - 14:59

score 118 · Answer 10 · 2026-03-26 10:59:59

118

Views

Paradox regarding the size of real numbers?

Published on 26 Mar 2026 - 10:59

score 42 · Answer 11 · 2023-05-26 13:40:41

42

Views

How to prove that the partial derivative with respect to x equals zero using derivative definition?

Published on 26 May 2023 - 13:40

score 73 · Answer 12 · 2023-05-27 17:31:49

73

Views

Convergence for infinite sum of all primorials reciprocals.

Published on 27 May 2023 - 17:31

score 574 · Answer 13 · 2023-05-29 18:36:06

574

Views

Infinite sets without subsets of some (finite) cardinalities?

Published on 29 May 2023 - 18:36

score 180 · Answer 14 · 2023-05-30 12:29:43

180

Views

Is it true that $\aleph_1=2^{\aleph_0}$, and if so, would the limit of $2^x$ as $x$ approaches $+\infty$ be equal to $\aleph_1$?

Published on 30 May 2023 - 12:29

score 273 · Answer 15 · 2023-06-04 17:03:37

273

Views

What makes an uncountable set "uncountable"?

Published on 04 Jun 2023 - 17:03

List Question

Evaluate $\lim_{n\ \rightarrow\ \infty\ }\ \left(\frac{\sqrt{1\times3}+\sqrt{2\times4}+\cdots\sqrt{n\times\left(n+2\right)}}{n}-\frac{n}{2}\right)$

Infinity times minus one

representing $\int_0^\infty{\frac{\sin x}{x^3}}dx$ in terms of $\int_0^\infty{\frac{\sin^3x}{x^3}}dx$

Why are the improper integrals $\int_{-\infty}^{\infty}x\,\mathrm{d}x$ and $\lim\limits_{n\to\infty} \int_{-n}^{n}x\,\mathrm{d}x$ different?

For infinite sets A,B do we also have $A\subseteq B\rightarrow|A|\leq|B|$?

What is the cardinality of the set of injective functions from $\mathbb{N}$ to $\mathcal P \mathbb{N}$?

Does this beginningless-past thought experiment result in several possible non-well-ordered sets?

What is truly infinity?

Does a recursive definition of a variable make sense at all?

Paradox regarding the size of real numbers?

How to prove that the partial derivative with respect to x equals zero using derivative definition?

Convergence for infinite sum of all primorials reciprocals.

Infinite sets without subsets of some (finite) cardinalities?

Is it true that $\aleph_1=2^{\aleph_0}$, and if so, would the limit of $2^x$ as $x$ approaches $+\infty$ be equal to $\aleph_1$?

What makes an uncountable set "uncountable"?

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