Question

Prove that $2^n = O(n!)$

score 50 · Answer 1 · 2026-04-16 05:33:11

50

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Prove that $2^n = O(n!)$

Published on 16 Apr 2026 - 5:33

score 1k · Answer 2 · 2026-04-15 07:06:01

1k

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Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

Published on 15 Apr 2026 - 7:06

score 127 · Answer 3 · 2026-04-14 20:54:50

127

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If $a, b \in \mathbb{N}$ are relatively prime, show that, for any $k \in \mathbb{N}$, $a^k$ and $b$ are relatively prime.

Published on 14 Apr 2026 - 20:54

score 624 · Answer 4 · 2026-04-12 20:47:25

624

Views

Divisibility via Induction: $8^n\mid (4n)!$

Published on 12 Apr 2026 - 20:47

score 182 · Answer 5 · 2026-04-17 02:40:43

182

Views

Proove $3^n$ divides $a(n)$ for all integers $n\ge 1$

Published on 17 Apr 2026 - 2:40

score 692 · Answer 6 · 2026-04-14 05:18:03

692

Views

Inequality for symmetric $n \times n$-matrix with non-negative elements.

Published on 14 Apr 2026 - 5:18

score 490 · Answer 7 · 2026-04-10 23:11:47

490

Views

An inequality with exponents, factorials and nth roots!

Published on 10 Apr 2026 - 23:11

score 471 · Answer 8 · 2026-04-13 20:41:02

471

Views

Simple proof of part of master theorem

Published on 13 Apr 2026 - 20:41

score 115 · Answer 9 · 2026-04-14 06:43:42

115

Views

Proving $\sum_{i=0}^n \binom{n}{i} = 2^n$ by math induction

Published on 14 Apr 2026 - 6:43

score 54 · Answer 10 · 2026-04-16 08:46:13

54

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Prove using induction that $\forall n \in \mathbb{N}$ $f(n) + g(n) = 1$

Published on 16 Apr 2026 - 8:46

score 12.3k · Answer 11 · 2026-04-15 05:36:06

12.3k

Views

Prove Using Induction: $\sum_{k=1}^{n} 1/k(k+1) = n/(n+1)$

Published on 15 Apr 2026 - 5:36

score 101 · Answer 12 · 2026-04-17 13:47:03

101

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Proving $1 \cdot 2 + 2 \cdot 3 + \cdots + n(n + 1) = 2\binom{n + 2}{3}$by math induction?

Published on 17 Apr 2026 - 13:47

score 123 · Answer 13 · 2026-04-17 02:54:41

123

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Show that $(a_1\cdot a_2\cdot ...\cdot a_n)^\frac 1n \leq (a_1+...+a_n)/n$

Published on 17 Apr 2026 - 2:54

score 178 · Answer 14 · 2026-04-15 01:01:06

178

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Prove using induction that $\forall x \in \Sigma^*$, $\operatorname{rev}(\operatorname{rev}(x)) = x$

Published on 15 Apr 2026 - 1:01

score 55.1k · Answer 15 · 2026-04-15 02:29:03

55.1k

Views

Proof by induction, 1 · 1! + 2 · 2! + ... + n · n! = (n + 1)! − 1

Published on 15 Apr 2026 - 2:29

List Question

Prove that $2^n = O(n!)$

Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

If $a, b \in \mathbb{N}$ are relatively prime, show that, for any $k \in \mathbb{N}$, $a^k$ and $b$ are relatively prime.

Divisibility via Induction: $8^n\mid (4n)!$

Proove $3^n$ divides $a(n)$ for all integers $n\ge 1$

Inequality for symmetric $n \times n$-matrix with non-negative elements.

An inequality with exponents, factorials and nth roots!

Simple proof of part of master theorem

Proving $\sum_{i=0}^n \binom{n}{i} = 2^n$ by math induction

Prove using induction that $\forall n \in \mathbb{N}$ $f(n) + g(n) = 1$

Prove Using Induction: $\sum_{k=1}^{n} 1/k(k+1) = n/(n+1)$

Proving $1 \cdot 2 + 2 \cdot 3 + \cdots + n(n + 1) = 2\binom{n + 2}{3}$by math induction?

Show that $(a_1\cdot a_2\cdot ...\cdot a_n)^\frac 1n \leq (a_1+...+a_n)/n$

Prove using induction that $\forall x \in \Sigma^*$, $\operatorname{rev}(\operatorname{rev}(x)) = x$

Proof by induction, 1 · 1! + 2 · 2! + ... + n · n! = (n + 1)! − 1

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