Question

Showing that a set of integers $A=\Bbb N^*$ where $A$ has two properties

score 31 · Answer 1 · 2020-07-24 15:53:04

31

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Showing that a set of integers $A=\Bbb N^*$ where $A$ has two properties

Published on 24 Jul 2020 - 15:53

score 131 · Answer 2 · 2026-04-11 04:16:33

131

Views

Proving the function is always positive in the interval $(0,1)$

Published on 11 Apr 2026 - 4:16

score 67 · Answer 3 · 2020-07-26 21:29:23

67

Views

Proofs by Induction: are my two proofs correct?

Published on 26 Jul 2020 - 21:29

score 85 · Answer 4 · 2020-07-27 00:52:22

85

Views

Proving that the sequence terms ${T_{n+1}}=T_n^2-T_n+1$ are relatively prime

Published on 27 Jul 2020 - 0:52

score 96 · Answer 5 · 2020-07-28 11:03:05

96

Views

Two nested proofs by induction: one inside the other (and co-dependent)

Published on 28 Jul 2020 - 11:03

score 54 · Answer 6 · 2020-07-28 20:20:20

54

Views

Given $a>0$, define inductively the sequence $x_n$ puting $x_1=1/a$ and $x_{n+1}=1/(a+x_n)$

Published on 28 Jul 2020 - 20:20

score 87 · Answer 7 · 2026-03-25 21:00:06

87

Views

Prove that $\mathrm{Ker}(T - \lambda I_V)^n = {0}$

Published on 25 Mar 2026 - 21:00

score 99 · Answer 8 · 2020-07-30 01:58:58

99

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Inductive step of $2^2 + 4^2 + \cdots + (2n)^2$

Published on 30 Jul 2020 - 1:58

score 2.8k · Answer 9 · 2026-04-11 02:02:46

2.8k

Views

Proof by Mathematical Induction for all natural numbers n.

Published on 11 Apr 2026 - 2:02

score 2.7k · Answer 10 · 2026-04-11 16:55:24

2.7k

Views

Principle Mathematical Induction Product Notation Question?

Published on 11 Apr 2026 - 16:55

score 7k · Answer 11 · 2016-07-06 03:30:25

7k

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Proving that $3+11 +19 + \cdots + (8n-5)= 4n^2 -n$ by induction

Published on 06 Jul 2016 - 3:30

score 2k · Answer 12 · 2026-04-11 18:52:34

2k

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Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers

Published on 11 Apr 2026 - 18:52

score 192 · Answer 13 · 2026-04-04 11:58:45

192

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Prove divisibility by induction $19\mid 5^{2n+1}2^{n+2}+3^{n+2}2^{2n+1}$

Published on 04 Apr 2026 - 11:58

score 4.6k · Answer 14 · 2016-07-06 16:19:08

4.6k

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Prove by induction that $n^5-5n^3+4n$ is divisible by 120 for all n starting from 3

Published on 06 Jul 2016 - 16:19

score 158 · Answer 15 · 2016-07-06 16:41:48

158

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Prove by induction that $a^{4n+1}-a$ is divisible by $30$ for any $a$ and $n \geq 1$

Published on 06 Jul 2016 - 16:41

List Question

Showing that a set of integers $A=\Bbb N^*$ where $A$ has two properties

Proving the function is always positive in the interval $(0,1)$

Proofs by Induction: are my two proofs correct?

Proving that the sequence terms ${T_{n+1}}=T_n^2-T_n+1$ are relatively prime

Two nested proofs by induction: one inside the other (and co-dependent)

Given $a>0$, define inductively the sequence $x_n$ puting $x_1=1/a$ and $x_{n+1}=1/(a+x_n)$

Prove that $\mathrm{Ker}(T - \lambda I_V)^n = {0}$

Inductive step of $2^2 + 4^2 + \cdots + (2n)^2$

Proof by Mathematical Induction for all natural numbers n.

Principle Mathematical Induction Product Notation Question?

Proving that $3+11 +19 + \cdots + (8n-5)= 4n^2 -n$ by induction

Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers

Prove divisibility by induction $19\mid 5^{2n+1}2^{n+2}+3^{n+2}2^{2n+1}$

Prove by induction that $n^5-5n^3+4n$ is divisible by 120 for all n starting from 3

Prove by induction that $a^{4n+1}-a$ is divisible by $30$ for any $a$ and $n \geq 1$

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