Question

Prove by double induction on $m,n$ that $(m+1)^n>mn\,\forall m,n\ge0.$

score 223 · Answer 1 · 2019-12-05 20:43:07

223

Views

Prove by double induction on $m,n$ that $(m+1)^n>mn\,\forall m,n\ge0.$

Published on 05 Dec 2019 - 20:43

score 307 · Answer 2 · 2019-12-05 22:44:57

307

Views

Show that $4^nx_n < 7^n$ for all positive integers $n$

Published on 05 Dec 2019 - 22:44

score 49 · Answer 3 · 2026-03-29 17:13:20

49

Views

Getting a closed form of this recurrence

Published on 29 Mar 2026 - 17:13

score 99 · Answer 4 · 2019-12-06 10:05:25

99

Views

Help with a mathematical induction problem

Published on 06 Dec 2019 - 10:05

score 47 · Answer 5 · 2019-12-06 13:03:32

47

Views

Induction of $\sum_{k=1}^n(2k-1)^2 = \frac{1}{3}n (2n-1)(2n+1), n \geq 1$

Published on 06 Dec 2019 - 13:03

score 98 · Answer 6 · 2019-12-06 13:35:48

98

Views

Proof explanation of $\sum_{k=0}^{n-1}(n+k)(n-k) = \frac{1}{6}n(n+1)(4n-1), n \geq 1$

Published on 06 Dec 2019 - 13:35

score 134 · Answer 7 · 2019-12-06 14:37:20

134

Views

Proof explanation of $5^{2n}-2^n$ is divisible by $23$ for $n \in \mathbb{N}$

Published on 06 Dec 2019 - 14:37

score 38 · Answer 8 · 2019-12-06 15:29:28

38

Views

Proof explanation of $\prod_{k=2}^n \big(1- \frac{2}{k(k+1)} \big) = \frac{1}{3} \big(1+\frac{2}{n} \big), n \geq 2$

Published on 06 Dec 2019 - 15:29

score 122 · Answer 9 · 2026-03-26 19:19:58

122

Views

Question About Part of the Proof of a Lemma to the Church-Rosser Theorem in "Lectures on the Curry-Howard Isomorphism"(1998)

Published on 26 Mar 2026 - 19:19

score 177 · Answer 10 · 2026-03-28 17:00:03

177

Views

proof : even nth Fibonacci number using Mathematical Induction

Published on 28 Mar 2026 - 17:00

score 77 · Answer 11 · 2019-12-07 17:55:27

77

Views

Use induction to prove that when $n≥1$, $a_i\in R$, $a_i > 0$, if $a_1a_2...a_n=1$, then $(1+a_1)(1+a_2)...(1+a_n)≥2^n$

Published on 07 Dec 2019 - 17:55

score 76 · Answer 12 · 2019-12-07 19:31:27

76

Views

Prove $\forall n \in \mathbb{N}, \sum\limits_{i=0}^{n-1} 2^i = 2^n -1$

Published on 07 Dec 2019 - 19:31

score 69 · Answer 13 · 2019-12-07 21:36:46

69

Views

Proving inequailty by induction

Published on 07 Dec 2019 - 21:36

score 39 · Answer 14 · 2019-12-09 06:50:20

39

Views

Where did the squared go in the 3rd line?

Published on 09 Dec 2019 - 6:50

score 252 · Answer 15 · 2019-12-09 18:14:33

252

Views

Strong Induction Proof Verification (n as a sum of 4s and 7s)

Published on 09 Dec 2019 - 18:14

List Question

Prove by double induction on $m,n$ that $(m+1)^n>mn\,\forall m,n\ge0.$

Show that $4^nx_n < 7^n$ for all positive integers $n$

Getting a closed form of this recurrence

Help with a mathematical induction problem

Induction of $\sum_{k=1}^n(2k-1)^2 = \frac{1}{3}n (2n-1)(2n+1), n \geq 1$

Proof explanation of $\sum_{k=0}^{n-1}(n+k)(n-k) = \frac{1}{6}n(n+1)(4n-1), n \geq 1$

Proof explanation of $5^{2n}-2^n$ is divisible by $23$ for $n \in \mathbb{N}$

Proof explanation of $\prod_{k=2}^n \big(1- \frac{2}{k(k+1)} \big) = \frac{1}{3} \big(1+\frac{2}{n} \big), n \geq 2$

Question About Part of the Proof of a Lemma to the Church-Rosser Theorem in "Lectures on the Curry-Howard Isomorphism"(1998)

proof : even nth Fibonacci number using Mathematical Induction

Use induction to prove that when $n≥1$, $a_i\in R$, $a_i > 0$, if $a_1a_2...a_n=1$, then $(1+a_1)(1+a_2)...(1+a_n)≥2^n$

Prove $\forall n \in \mathbb{N}, \sum\limits_{i=0}^{n-1} 2^i = 2^n -1$

Proving inequailty by induction

Where did the squared go in the 3rd line?

Strong Induction Proof Verification (n as a sum of 4s and 7s)

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