Question

How to prove: If $n \in N$, then $n^2=2\binom{n}{2} + \binom{n}{1}$

score 70 · Answer 1 · 2026-03-29 21:19:44

70

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How to prove: If $n \in N$, then $n^2=2\binom{n}{2} + \binom{n}{1}$

Published on 29 Mar 2026 - 21:19

score 550 · Answer 2 · 2026-03-27 15:19:23

550

Views

Prove that the class $\{A,A\} = \{A\}$ - does the axiom of class construction work in reverse to prove this?

Published on 27 Mar 2026 - 15:19

score 246 · Answer 3 · 2026-03-25 10:53:02

246

Views

Every subspace of a separable metric space is separable

Published on 25 Mar 2026 - 10:53

score 51 · Answer 4 · 2020-02-05 23:36:58

51

Views

How come $\{ \omega; S_N(\Omega) \in A \} = \cup_{k \in N} \{ \sum^{N(\omega)}_{i=1} X_i(\omega) \in A$ and $N(\omega)=k \}$

Published on 05 Feb 2020 - 23:36

score 226 · Answer 5 · 2020-02-06 00:04:51

226

Views

Prove or Disprove: There exists positive integers $x, y, z$, such that $x^8-y^5=z^3$

Published on 06 Feb 2020 - 0:04

score 68 · Answer 6 · 2020-02-06 09:12:31

68

Views

How to solve this non-linear 1st order differential equation?

Published on 06 Feb 2020 - 9:12

score 46 · Answer 7 · 2020-02-06 09:27:29

46

Views

How to prove that $g$ is continuous?

Published on 06 Feb 2020 - 9:27

score 39 · Answer 8 · 2020-02-06 09:46:57

39

Views

Where does $5$ come from in this case?

Published on 06 Feb 2020 - 9:46

score 54 · Answer 9 · 2026-03-29 22:41:16

54

Views

Find $\sup$ and $\inf$ of $\left\{\log_2\frac{10mn}{(2m+5n)^2}:m,n\in\mathbb N\right\}$

Published on 29 Mar 2026 - 22:41

score 60 · Answer 10 · 2026-03-26 12:40:36

60

Views

What is wrong with my solution about the completeness of this metric space?

Published on 26 Mar 2026 - 12:40

score 96 · Answer 11 · 2026-03-30 00:04:14

96

Views

Prove $a_n=\frac{(2^{n-1}+1)a_1-2^{n-1}+1}{2^{n-1}+1-(2^{n-1}-1)a_1}$ for the recursive sequence $a_{n+1}=\frac{3a_n-1}{3-a_n}$

Published on 30 Mar 2026 - 0:04

score 122 · Answer 12 · 2026-04-02 05:33:08

122

Views

Some well-known theorems about maximal-minimal

Published on 02 Apr 2026 - 5:33

score 47 · Answer 13 · 2020-02-06 15:13:10

47

Views

Finding the derivative of $N$ with respect to $t$ of $N=500(1-\frac{3}{(t^2+2)^2})$

Published on 06 Feb 2020 - 15:13

score 116 · Answer 14 · 2026-03-26 01:09:40

116

Views

Explicit cell structre of Torus with 3 points identified as 1

Published on 26 Mar 2026 - 1:09

score 45 · Answer 15 · 2026-04-02 12:24:26

45

Views

Proof verification of a property of greatest integer function

Published on 02 Apr 2026 - 12:24

List Question

How to prove: If $n \in N$, then $n^2=2\binom{n}{2} + \binom{n}{1}$

Prove that the class $\{A,A\} = \{A\}$ - does the axiom of class construction work in reverse to prove this?

Every subspace of a separable metric space is separable

How come $\{ \omega; S_N(\Omega) \in A \} = \cup_{k \in N} \{ \sum^{N(\omega)}_{i=1} X_i(\omega) \in A$ and $N(\omega)=k \}$

Prove or Disprove: There exists positive integers $x, y, z$, such that $x^8-y^5=z^3$

How to solve this non-linear 1st order differential equation?

How to prove that $g$ is continuous?

Where does $5$ come from in this case?

Find $\sup$ and $\inf$ of $\left\{\log_2\frac{10mn}{(2m+5n)^2}:m,n\in\mathbb N\right\}$

What is wrong with my solution about the completeness of this metric space?

Prove $a_n=\frac{(2^{n-1}+1)a_1-2^{n-1}+1}{2^{n-1}+1-(2^{n-1}-1)a_1}$ for the recursive sequence $a_{n+1}=\frac{3a_n-1}{3-a_n}$

Some well-known theorems about maximal-minimal

Finding the derivative of $N$ with respect to $t$ of $N=500(1-\frac{3}{(t^2+2)^2})$

Explicit cell structre of Torus with 3 points identified as 1

Proof verification of a property of greatest integer function

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