Question

How does $(k+1)!(k+2)(k+1)$ simplify to $(k+2)!(k+1)$

score 69 · Answer 1 · 2026-04-08 18:23:48

69

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How does $(k+1)!(k+2)(k+1)$ simplify to $(k+2)!(k+1)$

Published on 08 Apr 2026 - 18:23

score 96 · Answer 2 · 2026-04-09 18:53:00

96

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Proof By Induction - How to apply Induction Hypothesis?

Published on 09 Apr 2026 - 18:53

score 58 · Answer 3 · 2026-04-15 00:15:13

58

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Mathematical induction to prove equipotent sets. Schröder–Bernstein theorem

Published on 15 Apr 2026 - 0:15

score 104 · Answer 4 · 2026-03-26 08:23:03

104

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Suppose we want to prove that a property $P$ is true for every integer in $ℕ_{odd}$ = $\{1,3,5,7,9,...\}$.

Published on 26 Mar 2026 - 8:23

score 23 · Answer 5 · 2026-04-17 09:45:55

23

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Prove $\forall{m}\in \mathbb{N} - \{ 1 \}. \exists B_m \in \mathbb{N}. \forall{n} \in \mathbb{N}. n \geq B_m \implies n! > m^n$

Published on 17 Apr 2026 - 9:45

score 83 · Answer 6 · 2026-04-15 21:04:07

83

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Exercise 2.13 in Introduction to Set Theory, 3rd ed. by Hrbacek & Jech

Published on 15 Apr 2026 - 21:04

score 41 · Answer 7 · 2026-04-08 18:59:11

41

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Divisibility proof - alternative?

Published on 08 Apr 2026 - 18:59

score 108 · Answer 8 · 2026-04-15 23:34:55

108

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Prove that the statement $(1+2+3+ \cdots + n) \mid (1^m+2^m+3^m+ \cdots +n^m)$ is true for all odd numbers $m$

Published on 15 Apr 2026 - 23:34

score 1.2k · Answer 9 · 2026-04-10 07:43:58

1.2k

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Simplify sum of factorials with mathematical induction

Published on 10 Apr 2026 - 7:43

score 58 · Answer 10 · 2026-04-16 15:56:13

58

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Prove by induction that $\sum_{k=0}^{n}(-1)^{n+k} k^{2} = \frac{n(n+1)}{2}$

Published on 16 Apr 2026 - 15:56

score 52 · Answer 11 · 2026-04-15 19:49:17

Prove by induction that $\forall n \in \mathbb{N} \cup \{0\}: \sum_{k=0}^{n} \frac{k}{2^{k}} = 2 - \frac{n + 2}{2^{n}}$

score 375 · Answer 12 · 2026-04-25 11:48:03

375

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Show that ${n \choose k}\leq n^k$

Published on 25 Apr 2026 - 11:48

score 1k · Answer 13 · 2026-04-11 05:35:18

1k

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strong induction example

Published on 11 Apr 2026 - 5:35

score 100 · Answer 14 · 2026-04-11 21:54:55

100

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Simplexes in $\mathbb R^n$ have at most $n+1$ points

Published on 11 Apr 2026 - 21:54

score 47 · Answer 15 · 2026-04-14 23:39:58

47

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Proving by induction $3^{n-2}\le(n-1)! : \forall n\ge 6$

Published on 14 Apr 2026 - 23:39

List Question

How does $(k+1)!(k+2)(k+1)$ simplify to $(k+2)!(k+1)$

Proof By Induction - How to apply Induction Hypothesis?

Mathematical induction to prove equipotent sets. Schröder–Bernstein theorem

Suppose we want to prove that a property $P$ is true for every integer in $ℕ_{odd}$ = $\{1,3,5,7,9,...\}$.

Prove $\forall{m}\in \mathbb{N} - \{ 1 \}. \exists B_m \in \mathbb{N}. \forall{n} \in \mathbb{N}. n \geq B_m \implies n! > m^n$

Exercise 2.13 in Introduction to Set Theory, 3rd ed. by Hrbacek & Jech

Divisibility proof - alternative?

Prove that the statement $(1+2+3+ \cdots + n) \mid (1^m+2^m+3^m+ \cdots +n^m)$ is true for all odd numbers $m$

Simplify sum of factorials with mathematical induction

Prove by induction that $\sum_{k=0}^{n}(-1)^{n+k} k^{2} = \frac{n(n+1)}{2}$

Prove by induction that $\forall n \in \mathbb{N} \cup \{0\}: \sum_{k=0}^{n} \frac{k}{2^{k}} = 2 - \frac{n + 2}{2^{n}}$

Show that ${n \choose k}\leq n^k$

strong induction example

Simplexes in $\mathbb R^n$ have at most $n+1$ points

Proving by induction $3^{n-2}\le(n-1)! : \forall n\ge 6$

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