Question

How to prove that $(a+b-ab)^n+(1-a^n)(1-b^n) \geq n $ for $a,b\in [0,1]$ and $n\in\mathbb{N}$?

score 100 · Answer 1 · 2014-12-20 20:49:58

100

Views

How to prove that $(a+b-ab)^n+(1-a^n)(1-b^n) \geq n $ for $a,b\in [0,1]$ and $n\in\mathbb{N}$?

Published on 20 Dec 2014 - 20:49

score 85 · Answer 2 · 2014-12-22 04:46:51

85

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Question around the following relation: $T(n,1) = n$, for a positive integer $n$, and for all $k\geq 1,\ T(n,k+1)=n^{T(n,k)}$.

Published on 22 Dec 2014 - 4:46

score 388 · Answer 3 · 2014-12-22 10:23:00

388

Views

Induction proof that $2^m 2^n = 2^{m+n}$

Published on 22 Dec 2014 - 10:23

score 432 · Answer 4 · 2026-04-06 04:19:24

432

Views

How to prove that the sum of squared binomials equals $\binom{2n}{n}$

Published on 06 Apr 2026 - 4:19

score 3.8k · Answer 5 · 2014-12-22 21:07:03

3.8k

Views

Tips on constructing a proof by induction.

Published on 22 Dec 2014 - 21:07

score 107 · Answer 6 · 2014-12-22 22:39:15

107

Views

Induction on nth polynomial proof.

Published on 22 Dec 2014 - 22:39

score 739 · Answer 7 · 2026-03-25 14:08:18

739

Views

Inequality of the Fibonacci sequence and the golden ratio

Published on 25 Mar 2026 - 14:08

score 299 · Answer 8 · 2014-12-23 21:12:52

299

Views

Understanding the proof that the sum of the first $n$ natural numbers is $\frac{1}{2}n(n+1)$

Published on 23 Dec 2014 - 21:12

score 4.2k · Answer 9 · 2026-03-30 23:20:46

4.2k

Views

Why is "mathematical induction" called "mathematical"?

Published on 30 Mar 2026 - 23:20

score 177 · Answer 10 · 2026-03-27 21:51:21

177

Views

Cauchy convergence criterion for the sequence $x_{n+1}=\frac{x_n+x_{n-1}}{2}$

Published on 27 Mar 2026 - 21:51

score 93 · Answer 11 · 2026-03-29 08:16:01

93

Views

Proving that $\sum_{i=0}^{n-p} \frac{i!}{(p+i)!} = \frac{1}{p-1}[\frac{1}{(p-1)!}-\frac{(n-p+1)!}{n!}]$

Published on 29 Mar 2026 - 8:16

score 225 · Answer 12 · 2014-12-27 11:14:11

225

Views

Proving inequality $\frac{n}{2} < 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + + \frac{1}{2^{n}-1} < n$

Published on 27 Dec 2014 - 11:14

score 764 · Answer 13 · 2026-03-26 18:59:02

764

Views

Using induction to prove a congruence?

Published on 26 Mar 2026 - 18:59

score 148 · Answer 14 · 2014-12-28 12:18:53

148

Views

Strong induction. What is responsible for basis step?

Published on 28 Dec 2014 - 12:18

score 69 · Answer 15 · 2014-12-28 14:58:36

69

Views

Show that $(1+a_1x+\ldots+a_rx^r)^k=1+x+x^{r+1}q(x)$

Published on 28 Dec 2014 - 14:58

List Question

How to prove that $(a+b-ab)^n+(1-a^n)(1-b^n) \geq n $ for $a,b\in [0,1]$ and $n\in\mathbb{N}$?

Question around the following relation: $T(n,1) = n$, for a positive integer $n$, and for all $k\geq 1,\ T(n,k+1)=n^{T(n,k)}$.

Induction proof that $2^m 2^n = 2^{m+n}$

How to prove that the sum of squared binomials equals $\binom{2n}{n}$

Tips on constructing a proof by induction.

Induction on nth polynomial proof.

Inequality of the Fibonacci sequence and the golden ratio

Understanding the proof that the sum of the first $n$ natural numbers is $\frac{1}{2}n(n+1)$

Why is "mathematical induction" called "mathematical"?

Cauchy convergence criterion for the sequence $x_{n+1}=\frac{x_n+x_{n-1}}{2}$

Proving that $\sum_{i=0}^{n-p} \frac{i!}{(p+i)!} = \frac{1}{p-1}[\frac{1}{(p-1)!}-\frac{(n-p+1)!}{n!}]$

Proving inequality $\frac{n}{2} < 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + + \frac{1}{2^{n}-1} < n$

Using induction to prove a congruence?

Strong induction. What is responsible for basis step?

Show that $(1+a_1x+\ldots+a_rx^r)^k=1+x+x^{r+1}q(x)$

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