Question

How is 2 considered a product of primes.

score 108 · Answer 1 · 2026-04-13 22:51:12

108

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How is 2 considered a product of primes.

Published on 13 Apr 2026 - 22:51

score 44 · Answer 2 · 2026-04-12 18:40:45

44

Views

Alternative formation/ notation for axiom of mathematical induction

Published on 12 Apr 2026 - 18:40

score 56 · Answer 3 · 2026-04-14 14:18:20

56

Views

Some proof by induction

Published on 14 Apr 2026 - 14:18

score 89 · Answer 4 · 2026-04-14 15:46:27

89

Views

Series Conversion, Jacobsthal Sequence

Published on 14 Apr 2026 - 15:46

score 113 · Answer 5 · 2026-04-16 02:33:39

113

Views

Prove by induction $(6^ − 1)(7^ − 1)$ is a multiple of $30$ for all natural number $n$

Published on 16 Apr 2026 - 2:33

score 56 · Answer 6 · 2026-04-16 07:31:55

56

Views

Prove sum of heights of complete binary tree is $N - b(N)$

Published on 16 Apr 2026 - 7:31

score 46 · Answer 7 · 2026-04-14 03:51:22

46

Views

Prove property of a sequence

Published on 14 Apr 2026 - 3:51

score 120 · Answer 8 · 2026-04-13 16:39:13

120

Views

How to solve with mathematical induction $\left(1+ \dfrac{1}{n}\right)^n <3$

Published on 13 Apr 2026 - 16:39

score 99 · Answer 9 · 2026-04-15 11:31:29

99

Views

Prove by induction: Let $r \in \mathbb{N}$. $\exists a_{r,1}, \ldots, a_{r,r} \in \mathbb{Q} \, \forall n \in \mathbb{N}$

Published on 15 Apr 2026 - 11:31

score 112 · Answer 10 · 2026-04-16 03:41:59

112

Views

prove that $k\leq 2n$ when $v_1,\cdots, v_k$ are nonzero vectors in $\mathbb{R}^n$ so that $v_i^T v_j\leq 0$ for $i\neq j$

Published on 16 Apr 2026 - 3:41

score 108 · Answer 11 · 2026-04-17 08:48:13

108

Views

Let $a_n$ be a sequence satisfying $a_1 = a_2 = 1$, and $a_n = \frac{1}{2}(a_{n-1} + \frac{2}{a_{n-2}})$ for $n \ge 3$. Prove that $1\le a_n\le 2$.

Published on 17 Apr 2026 - 8:48

score 51 · Answer 12 · 2026-04-16 23:19:47

51

Views

Prove that for any real number $x, \sum_{i=1}^n a_i \lfloor ix \rfloor\ge 0$

Published on 16 Apr 2026 - 23:19

score 98 · Answer 13 · 2026-04-15 09:34:31

98

Views

Prove that $\sum_{n=1}^\infty \dfrac{1}{\log_2(a_n)}$ converges.

Published on 15 Apr 2026 - 9:34

score 56 · Answer 14 · 2026-04-13 20:18:06

56

Views

$ \forall n \in N: \forall m \in N: n<m \Rightarrow \exists r \in N: n+r=m$

Published on 13 Apr 2026 - 20:18

score 102 · Answer 15 · 2026-04-16 10:52:19

102

Views

Prove that for any $n \in \mathbb{N}$, $\sum_{k=1}^n k^2(k+1)=\dfrac{n(n+1)(n+2)(3n+1)}{12}$

Published on 16 Apr 2026 - 10:52

List Question

How is 2 considered a product of primes.

Alternative formation/ notation for axiom of mathematical induction

Some proof by induction

Series Conversion, Jacobsthal Sequence

Prove by induction $(6^ − 1)(7^ − 1)$ is a multiple of $30$ for all natural number $n$

Prove sum of heights of complete binary tree is $N - b(N)$

Prove property of a sequence

How to solve with mathematical induction $\left(1+ \dfrac{1}{n}\right)^n <3$

Prove by induction: Let $r \in \mathbb{N}$. $\exists a_{r,1}, \ldots, a_{r,r} \in \mathbb{Q} \, \forall n \in \mathbb{N}$

prove that $k\leq 2n$ when $v_1,\cdots, v_k$ are nonzero vectors in $\mathbb{R}^n$ so that $v_i^T v_j\leq 0$ for $i\neq j$

Let $a_n$ be a sequence satisfying $a_1 = a_2 = 1$, and $a_n = \frac{1}{2}(a_{n-1} + \frac{2}{a_{n-2}})$ for $n \ge 3$. Prove that $1\le a_n\le 2$.

Prove that for any real number $x, \sum_{i=1}^n a_i \lfloor ix \rfloor\ge 0$

Prove that $\sum_{n=1}^\infty \dfrac{1}{\log_2(a_n)}$ converges.

$ \forall n \in N: \forall m \in N: n<m \Rightarrow \exists r \in N: n+r=m$

Prove that for any $n \in \mathbb{N}$, $\sum_{k=1}^n k^2(k+1)=\dfrac{n(n+1)(n+2)(3n+1)}{12}$

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