Question

Prove that $\frac{(2+{\sqrt 3})^{2k-1}+(2-{\sqrt 3})^{2k-1}}{2}-1$ always results in a square number

score 145 · Answer 1 · 2020-06-08 17:40:25

145

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Prove that $\frac{(2+{\sqrt 3})^{2k-1}+(2-{\sqrt 3})^{2k-1}}{2}-1$ always results in a square number

Published on 08 Jun 2020 - 17:40

score 187 · Answer 2 · 2020-06-08 19:26:57

187

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Induction Proof that $ x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1}).$

Published on 08 Jun 2020 - 19:26

score 47 · Answer 3 · 2020-06-10 02:31:21

47

Views

Proving That $\sum^{n}_{k=0} \bigl(\frac{4}{5}\bigr)^k < 5$

Published on 10 Jun 2020 - 2:31

score 161 · Answer 4 · 2026-04-11 12:44:17

161

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A Question About The Tower Of Hanoi

Published on 11 Apr 2026 - 12:44

score 54 · Answer 5 · 2026-04-11 00:01:53

54

Views

Question About An Induction Problem: What Am I Supposed To Prove?

Published on 11 Apr 2026 - 0:01

score 34 · Answer 6 · 2026-03-26 12:45:20

34

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$\forall x \in X: (y < x \implies y \in E) \implies x \in E$

Published on 26 Mar 2026 - 12:45

score 33 · Answer 7 · 2020-06-10 15:10:35

33

Views

I do not understand an inequliaty that is used to prove the ratio test

Published on 10 Jun 2020 - 15:10

score 61 · Answer 8 · 2026-04-11 07:02:10

61

Views

How to end showing that a statement is true by using induction?

Published on 11 Apr 2026 - 7:02

score 367 · Answer 9 · 2020-06-11 14:53:55

367

Views

$a_{m+n}+a_{m-n}=\frac{1}{2}(a_{2m}+a_{2n}), a_1=1$, find $ a_{1995}$

Published on 11 Jun 2020 - 14:53

score 186 · Answer 10 · 2020-06-12 14:19:32

186

Views

$f(n)=n+\lfloor\sqrt{n}\rfloor$. Prove for all $m\in \mathbb{N}$, the sequence $m,f(m),f(f(m)),..$ contains a perfect square

Published on 12 Jun 2020 - 14:19

score 77 · Answer 11 · 2020-06-12 14:25:55

77

Views

Prove derivative by induction

Published on 12 Jun 2020 - 14:25

score 79 · Answer 12 · 2026-04-10 00:42:04

79

Views

What is the importance of the word "inductively"? can I omit it?

Published on 10 Apr 2026 - 0:42

score 44 · Answer 13 · 2020-06-12 20:45:09

44

Views

simple/complete induction

Published on 12 Jun 2020 - 20:45

score 30 · Answer 14 · 2020-06-13 16:16:08

30

Views

Number set with induction

Published on 13 Jun 2020 - 16:16

score 187 · Answer 15 · 2026-04-09 21:17:19

187

Views

What is the problem with this proof of the PMI?

Published on 09 Apr 2026 - 21:17

List Question

Prove that $\frac{(2+{\sqrt 3})^{2k-1}+(2-{\sqrt 3})^{2k-1}}{2}-1$ always results in a square number

Induction Proof that $ x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1}).$

Proving That $\sum^{n}_{k=0} \bigl(\frac{4}{5}\bigr)^k < 5$

A Question About The Tower Of Hanoi

Question About An Induction Problem: What Am I Supposed To Prove?

$\forall x \in X: (y < x \implies y \in E) \implies x \in E$

I do not understand an inequliaty that is used to prove the ratio test

How to end showing that a statement is true by using induction?

$a_{m+n}+a_{m-n}=\frac{1}{2}(a_{2m}+a_{2n}), a_1=1$, find $ a_{1995}$

$f(n)=n+\lfloor\sqrt{n}\rfloor$. Prove for all $m\in \mathbb{N}$, the sequence $m,f(m),f(f(m)),..$ contains a perfect square

Prove derivative by induction

What is the importance of the word "inductively"? can I omit it?

simple/complete induction

Number set with induction

What is the problem with this proof of the PMI?

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