Question

Examples where Strong Induction is more useful than "Regular" Induction?

score 298 · Answer 1 · 2018-09-29 07:43:25

298

Views

Examples where Strong Induction is more useful than "Regular" Induction?

Published on 29 Sep 2018 - 7:43

score 513 · Answer 2 · 2026-03-26 01:00:04

513

Views

Demonstration inclusion - exclusion by induction for n elements.

Published on 26 Mar 2026 - 1:00

score 33 · Answer 3 · 2018-09-29 18:35:24

33

Views

Let $a_{n+1}=a_n-a_n^3$ with $a_1=\frac{1}{3}$. Show that $a_n>0$ for all $n\in\mathbb{N}$

Published on 29 Sep 2018 - 18:35

score 137 · Answer 4 · 2026-03-26 04:51:59

137

Views

What Quantifier is Used When Assuming P(n) for some n, in the Induction Hypothesis?

Published on 26 Mar 2026 - 4:51

score 86 · Answer 5 · 2018-09-30 16:44:08

86

Views

How to show that $\dfrac{n^3 + 2n}{3}$ is an integer

Published on 30 Sep 2018 - 16:44

score 44 · Answer 6 · 2018-09-30 17:29:48

44

Views

Guessing a general form for a recursive sequence

Published on 30 Sep 2018 - 17:29

score 1.3k · Answer 7 · 2018-09-30 19:46:20

1.3k

Views

Showing that if n is a natural number larger than 3, then $n!>2^n$

Published on 30 Sep 2018 - 19:46

score 1.1k · Answer 8 · 2018-09-30 20:13:05

1.1k

Views

Prove by induction that, for all positive integers n, the following inequality holds:

Published on 30 Sep 2018 - 20:13

score 45 · Answer 9 · 2018-10-01 00:24:08

45

Views

Let $a$ be an odd integer. Using induction, prove: For any $n\in\mathbb{Z}^+$, $a^{2^n}\equiv 1\mod{2^{n+2}}$

Published on 01 Oct 2018 - 0:24

score 126 · Answer 10 · 2018-10-01 00:58:18

126

Views

A strange inductive proof: Induction on $n$, for all positive integers $n,n\ge1$

Published on 01 Oct 2018 - 0:58

score 145 · Answer 11 · 2018-10-01 02:38:41

145

Views

By induction showing that $m^3\le2^m$ for $m\ge10$

Published on 01 Oct 2018 - 2:38

score 67 · Answer 12 · 2026-03-26 06:09:15

67

Views

Induction Proof clarifications, and how to define abstract relations

Published on 26 Mar 2026 - 6:09

score 211 · Answer 13 · 2026-03-28 12:32:46

211

Views

Find determinant of matrix $a_{ij} = 1$ if $i<j-1,$ $a_{ij} = 0$ if $i=j-1,$ $a_{ij} = -1$ if $i>j-1.$

Published on 28 Mar 2026 - 12:32

score 902 · Answer 14 · 2026-03-25 23:38:06

902

Views

Proof of Poincare's Inclusion-Exclusion Indicator Function Formula by Induction

Published on 25 Mar 2026 - 23:38

score 40 · Answer 15 · 2026-03-26 04:50:42

40

Views

'Transforming' a function $T(m,n)$ into $a(n)$ in an inductive proof

Published on 26 Mar 2026 - 4:50

List Question

Examples where Strong Induction is more useful than "Regular" Induction?

Demonstration inclusion - exclusion by induction for n elements.

Let $a_{n+1}=a_n-a_n^3$ with $a_1=\frac{1}{3}$. Show that $a_n>0$ for all $n\in\mathbb{N}$

What Quantifier is Used When Assuming P(n) for some n, in the Induction Hypothesis?

How to show that $\dfrac{n^3 + 2n}{3}$ is an integer

Guessing a general form for a recursive sequence

Showing that if n is a natural number larger than 3, then $n!>2^n$

Prove by induction that, for all positive integers n, the following inequality holds:

Let $a$ be an odd integer. Using induction, prove: For any $n\in\mathbb{Z}^+$, $a^{2^n}\equiv 1\mod{2^{n+2}}$

A strange inductive proof: Induction on $n$, for all positive integers $n,n\ge1$

By induction showing that $m^3\le2^m$ for $m\ge10$

Induction Proof clarifications, and how to define abstract relations

Find determinant of matrix $a_{ij} = 1$ if $i<j-1,$ $a_{ij} = 0$ if $i=j-1,$ $a_{ij} = -1$ if $i>j-1.$

Proof of Poincare's Inclusion-Exclusion Indicator Function Formula by Induction

'Transforming' a function $T(m,n)$ into $a(n)$ in an inductive proof

Trending Questions

Popular # Hahtags

Popular Questions