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Why is mathematical induction a valid proof technique?

score 18.9k · Answer 1 · 2026-04-10 20:09:15

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Why is mathematical induction a valid proof technique?

Published on 10 Apr 2026 - 20:09

score 793 · Answer 2 · 2026-04-11 19:53:52

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Prove by induction that $n^2<n!$

Published on 11 Apr 2026 - 19:53

score 50 · Answer 3 · 2026-04-16 01:19:16

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Induction. $\forall k\in \Bbb N , \sum^{2k-1}_{n=k}\frac{n}{2^n}=\frac{(2k+2)2^k-4k-2}{2^{2k}}$

Published on 16 Apr 2026 - 1:19

score 311 · Answer 4 · 2026-04-15 22:23:47

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Proof: $2\sqrt{m}-2 < \sum\limits_{n=1}^m\frac{1}{\sqrt{n}}< 2\sqrt{m}-1$

Published on 15 Apr 2026 - 22:23

score 176 · Answer 5 · 2026-04-10 07:33:25

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Question about induction to infinity with regard to Bolzano's philosophy

Published on 10 Apr 2026 - 7:33

score 39 · Answer 6 · 2026-04-11 08:51:34

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Can induction be used for $n \leq 0 $

Published on 11 Apr 2026 - 8:51

score 6.6k · Answer 7 · 2026-04-12 15:54:43

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Proof by induction and combinations

Published on 12 Apr 2026 - 15:54

score 1.9k · Answer 8 · 2026-04-25 21:11:43

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Proof by induction (combinations): $\binom n1 =n$ and $\binom n{n-1}=n$

Published on 25 Apr 2026 - 21:11

score 74 · Answer 9 · 2026-04-17 14:36:23

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Prove that $ exp_{a}(\frac{p}{q}) = \sqrt[q]{a^{p}} \space \forall \space p,q \in \mathbb{Z} $

Published on 17 Apr 2026 - 14:36

score 375 · Answer 10 · 2026-04-10 07:48:03

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Stirling Numbers of First Kind Proof by Induction

Published on 10 Apr 2026 - 7:48

score 140 · Answer 11 · 2026-04-16 10:41:27

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Proof by induction; inequality $1\cdot3+2\cdot4+3\cdot5+\dots+n(n+2) \ge \frac{n^3+5n}3$

Published on 16 Apr 2026 - 10:41

score 97 · Answer 12 · 2026-04-14 10:17:22

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Mathematical induction final step -- proving $n^3 \leq 2^n$, where $n\geq 10$

Published on 14 Apr 2026 - 10:17

score 148 · Answer 13 · 2026-04-13 13:15:46

148

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Induction exercise check-up

Published on 13 Apr 2026 - 13:15

score 706 · Answer 14 · 2026-04-15 17:21:02

706

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Proving $\frac{n^n}{e^{n-1}}<n!<\frac{(n+1)^{n+1}}{e^{n}}$ by induction for all $n> 2$.

Published on 15 Apr 2026 - 17:21

score 102 · Answer 15 · 2026-04-12 10:25:08

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Usage of Mathematical Induction

Published on 12 Apr 2026 - 10:25

List Question

Why is mathematical induction a valid proof technique?

Prove by induction that $n^2<n!$

Induction. $\forall k\in \Bbb N , \sum^{2k-1}_{n=k}\frac{n}{2^n}=\frac{(2k+2)2^k-4k-2}{2^{2k}}$

Proof: $2\sqrt{m}-2 < \sum\limits_{n=1}^m\frac{1}{\sqrt{n}}< 2\sqrt{m}-1$

Question about induction to infinity with regard to Bolzano's philosophy

Can induction be used for $n \leq 0 $

Proof by induction and combinations

Proof by induction (combinations): $\binom n1 =n$ and $\binom n{n-1}=n$

Prove that $ exp_{a}(\frac{p}{q}) = \sqrt[q]{a^{p}} \space \forall \space p,q \in \mathbb{Z} $

Stirling Numbers of First Kind Proof by Induction

Proof by induction; inequality $1\cdot3+2\cdot4+3\cdot5+\dots+n(n+2) \ge \frac{n^3+5n}3$

Mathematical induction final step -- proving $n^3 \leq 2^n$, where $n\geq 10$

Induction exercise check-up

Proving $\frac{n^n}{e^{n-1}}<n!<\frac{(n+1)^{n+1}}{e^{n}}$ by induction for all $n> 2$.

Usage of Mathematical Induction

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