Question

Is the concatenation operation on a list associative?

score 621 · Answer 1 · 2026-04-13 13:26:54

621

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Is the concatenation operation on a list associative?

Published on 13 Apr 2026 - 13:26

score 94 · Answer 2 · 2026-04-16 11:01:27

94

Views

Prove this inequality by induction

Published on 16 Apr 2026 - 11:01

score 99 · Answer 3 · 2026-04-15 08:13:41

99

Views

$f(x)\in\mathbb{Q}[x]$ such that $f(\mathbb{Z})\subseteq \mathbb{Z}$ Then show that $f$ has the following form

Published on 15 Apr 2026 - 8:13

score 2.6k · Answer 4 · 2026-04-15 19:41:49

2.6k

Views

$2 \cdot 4^{2n + 1} + 3^{3n + 1}$ is divisible by $\lambda$, for all $n \in N$. Find $\lambda$.

Published on 15 Apr 2026 - 19:41

score 8.2k · Answer 5 · 2026-04-15 16:21:31

8.2k

Views

Prove Big-Oh using Induction

Published on 15 Apr 2026 - 16:21

score 119 · Answer 6 · 2026-04-17 10:18:00

119

Views

Prove that $3^n|4^{3^{n-1}}-1$, but $3^{n+1}\not|4^{3^{n-1}}-1$ for all $n\in\mathbb N$.

Published on 17 Apr 2026 - 10:18

score 65 · Answer 7 · 2026-04-11 20:48:33

65

Views

Geometric summation question

Published on 11 Apr 2026 - 20:48

score 114 · Answer 8 · 2026-04-13 16:28:39

114

Views

Showing inequalities hold within a partial order on $\mathbb{R}[x]$

Published on 13 Apr 2026 - 16:28

score 583 · Answer 9 · 2026-04-11 16:34:08

583

Views

Mathematical Induction for an alternating series

Published on 11 Apr 2026 - 16:34

score 511 · Answer 10 · 2026-04-16 18:50:16

511

Views

Prove that $a^n-b^n \geq (a-b)nb^{n-1}$ where $a \geq b \geq 0$

Published on 16 Apr 2026 - 18:50

score 78 · Answer 11 · 2026-04-15 14:00:13

78

Views

Use induction to prove that the inequality, $n! < \left(\frac{n}{2}\right)^n$ continues to hold after $n=6$.

Published on 15 Apr 2026 - 14:00

score 693 · Answer 12 · 2026-04-17 22:32:45

693

Views

Prove $a_n = n 3^{n-1}$, recurrence relation.

Published on 17 Apr 2026 - 22:32

score 134 · Answer 13 · 2026-04-15 05:31:09

134

Views

Prove that $\sum_{i=1}^n (1+2+3+...+i)r^i < \frac{1}{(1-r)^3}$ for all $n\ge1$ and $0\lt r\lt1$

Published on 15 Apr 2026 - 5:31

score 496 · Answer 14 · 2026-04-12 04:42:39

496

Views

Proving that two structures are elementarily equivalent using the Tarski-Vaught Test

Published on 12 Apr 2026 - 4:42

score 1.5k · Answer 15 · 2026-04-16 08:19:47

1.5k

Views

If $49^n + 16^n +k$ is divisible by $64$ then find $k$.

Published on 16 Apr 2026 - 8:19

List Question

Is the concatenation operation on a list associative?

Prove this inequality by induction

$f(x)\in\mathbb{Q}[x]$ such that $f(\mathbb{Z})\subseteq \mathbb{Z}$ Then show that $f$ has the following form

$2 \cdot 4^{2n + 1} + 3^{3n + 1}$ is divisible by $\lambda$, for all $n \in N$. Find $\lambda$.

Prove Big-Oh using Induction

Prove that $3^n|4^{3^{n-1}}-1$, but $3^{n+1}\not|4^{3^{n-1}}-1$ for all $n\in\mathbb N$.

Geometric summation question

Showing inequalities hold within a partial order on $\mathbb{R}[x]$

Mathematical Induction for an alternating series

Prove that $a^n-b^n \geq (a-b)nb^{n-1}$ where $a \geq b \geq 0$

Use induction to prove that the inequality, $n! < \left(\frac{n}{2}\right)^n$ continues to hold after $n=6$.

Prove $a_n = n 3^{n-1}$, recurrence relation.

Prove that $\sum_{i=1}^n (1+2+3+...+i)r^i < \frac{1}{(1-r)^3}$ for all $n\ge1$ and $0\lt r\lt1$

Proving that two structures are elementarily equivalent using the Tarski-Vaught Test

If $49^n + 16^n +k$ is divisible by $64$ then find $k$.

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