Question

Proving a sequence by induction

score 121 · Answer 1 · 2018-04-04 18:46:24

121

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Proving a sequence by induction

Published on 04 Apr 2018 - 18:46

score 127 · Answer 2 · 2026-03-26 03:11:25

127

Views

Induction regarding Stirling numbers of the second kind.

Published on 26 Mar 2026 - 3:11

score 352 · Answer 3 · 2018-04-05 18:19:20

Prove that all positive integers $n$, $(1-{\sqrt 5})^n$ can be written in the form $a-b{\sqrt 5}$ where $a$ and $b$ are positive integers

score 144 · Answer 4 · 2018-04-05 20:40:28

144

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Proof by induction base case incorrect?

Published on 05 Apr 2018 - 20:40

score 118 · Answer 5 · 2026-03-25 08:09:42

118

Views

Prove using mathematical induction $1\cdot2+2\cdot2^2+3\cdot2^3+\ldots+n\cdot2^n=2[1+(n-1)2^n]$

Published on 25 Mar 2026 - 8:09

score 134 · Answer 6 · 2018-04-06 04:05:26

134

Views

Prove by induction $4$ is a divisor of $(3^n +2n-1)\; ,n\ge1$

Published on 06 Apr 2018 - 4:05

score 621 · Answer 7 · 2018-04-06 20:53:30

621

Views

Proving convergence of inductively defined sequence

Published on 06 Apr 2018 - 20:53

score 870 · Answer 8 · 2018-04-07 05:52:57

870

Views

Proving any integer cube is equal to a difference of two squares

Published on 07 Apr 2018 - 5:52

score 87 · Answer 9 · 2026-03-25 17:26:09

87

Views

Mathematical induction proof that each tree has $k = m − 1$ edges

Published on 25 Mar 2026 - 17:26

score 421 · Answer 10 · 2026-03-25 14:16:45

421

Views

Use Strong Induction on the number of times the recursive step is applied to show that $a \le 2b$ each time $(a,b)$ is an element of the set $S$

Published on 25 Mar 2026 - 14:16

score 74 · Answer 11 · 2018-04-07 19:38:16

74

Views

Help with equation manipulation when performing inductive proof.

Published on 07 Apr 2018 - 19:38

score 2.7k · Answer 12 · 2018-04-08 11:15:36

2.7k

Views

Prove by induction that $(z^n)^=(z^)^n$ for all positive integers of n

Published on 08 Apr 2018 - 11:15

score 417 · Answer 13 · 2018-04-08 20:19:43

417

Views

Induction in proof of Rule of Substitution

Published on 08 Apr 2018 - 20:19

score 84 · Answer 14 · 2018-04-09 01:49:29

84

Views

Proof by Induction $\frac{n+1}{2n} = \left(1-\frac{1}{2^2}\right)\dotsc \left(1-\frac{1}{n^2}\right)$

Published on 09 Apr 2018 - 1:49

score 271 · Answer 15 · 2018-04-09 01:57:46

271

Views

How to represent a directed acyclic graph in a way that makes it easy to conduct an inductive proof?

Published on 09 Apr 2018 - 1:57

List Question

Proving a sequence by induction

Induction regarding Stirling numbers of the second kind.

Prove that all positive integers $n$, $(1-{\sqrt 5})^n$ can be written in the form $a-b{\sqrt 5}$ where $a$ and $b$ are positive integers

Proof by induction base case incorrect?

Prove using mathematical induction $1\cdot2+2\cdot2^2+3\cdot2^3+\ldots+n\cdot2^n=2[1+(n-1)2^n]$

Prove by induction $4$ is a divisor of $(3^n +2n-1)\; ,n\ge1$

Proving convergence of inductively defined sequence

Proving any integer cube is equal to a difference of two squares

Mathematical induction proof that each tree has $k = m − 1$ edges

Use Strong Induction on the number of times the recursive step is applied to show that $a \le 2b$ each time $(a,b)$ is an element of the set $S$

Help with equation manipulation when performing inductive proof.

Prove by induction that $(z^n)^=(z^)^n$ for all positive integers of n

Induction in proof of Rule of Substitution

Proof by Induction $\frac{n+1}{2n} = \left(1-\frac{1}{2^2}\right)\dotsc \left(1-\frac{1}{n^2}\right)$

How to represent a directed acyclic graph in a way that makes it easy to conduct an inductive proof?

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