Question

Proof by induction for $2^{n+1} < 1 + (n+1)\times 2^n$ for $n \geq 1$

score 45 · Answer 1 · 2018-11-01 14:03:19

45

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Proof by induction for $2^{n+1} < 1 + (n+1)\times 2^n$ for $n \geq 1$

Published on 01 Nov 2018 - 14:03

score 122 · Answer 2 · 2018-11-01 14:22:51

122

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$2 < (1 + \frac{1}{n})^n < 3$ for all $n > 2$

Published on 01 Nov 2018 - 14:22

score 1.3k · Answer 3 · 2018-11-01 14:40:29

1.3k

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Strong inductive proof of division algorithm (quotient with remainder)

Published on 01 Nov 2018 - 14:40

score 163 · Answer 4 · 2018-11-01 21:29:59

163

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How to prove by induction that $10^n = 3m+1$

Published on 01 Nov 2018 - 21:29

score 572 · Answer 5 · 2018-11-02 00:43:08

572

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For every natural number $m$, $2^{2m}-1$ is divisible by $3$

Published on 02 Nov 2018 - 0:43

score 32 · Answer 6 · 2026-03-27 00:01:49

32

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Small induction problem.

Published on 27 Mar 2026 - 0:01

score 70 · Answer 7 · 2018-11-02 03:54:32

70

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How to prove the following claim using structural induction?

Published on 02 Nov 2018 - 3:54

score 261 · Answer 8 · 2026-03-26 21:12:38

261

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Prove $(1+\sqrt{2})^k= \sqrt{n}+\sqrt{n-1}$

Published on 26 Mar 2026 - 21:12

score 69 · Answer 9 · 2018-11-02 13:25:56

69

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Prove $\sum_{k=0}^n 2^{-k} = \frac{2^{n+1}-1}{2^n}$

Published on 02 Nov 2018 - 13:25

score 85 · Answer 10 · 2018-11-03 04:45:59

85

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Proof by induction of summation inequality: $1 + 1/2+ 1/3+ 1/4+1/5+⋯+ 1/2^n \leq n + 1$

Published on 03 Nov 2018 - 4:45

score 206 · Answer 11 · 2026-03-25 12:50:00

206

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Prove $\left(1-\frac{1}{n^2}\right)^n\times\left(1+\frac 1n\right)<1$ for every natural $n > 0$ by induction

Published on 25 Mar 2026 - 12:50

score 587 · Answer 12 · 2026-03-25 07:38:25

587

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Inductive Proof With Regular Expression

Published on 25 Mar 2026 - 7:38

score 69 · Answer 13 · 2018-11-03 16:02:24

69

Views

Mathematical Proof By Induction of $1 + 2 +\dots + n = (n + 1)n/2$

Published on 03 Nov 2018 - 16:02

score 1k · Answer 14 · 2026-03-25 07:42:03

1k

Views

Is induction something we take on faith?

Published on 25 Mar 2026 - 7:42

score 1k · Answer 15 · 2018-11-04 05:22:07

1k

Views

Connectivity in a graph with even-degree vertices is preserved by edge removal

Published on 04 Nov 2018 - 5:22

List Question

Proof by induction for $2^{n+1} < 1 + (n+1)\times 2^n$ for $n \geq 1$

$2 < (1 + \frac{1}{n})^n < 3$ for all $n > 2$

Strong inductive proof of division algorithm (quotient with remainder)

How to prove by induction that $10^n = 3m+1$

For every natural number $m$, $2^{2m}-1$ is divisible by $3$

Small induction problem.

How to prove the following claim using structural induction?

Prove $(1+\sqrt{2})^k= \sqrt{n}+\sqrt{n-1}$

Prove $\sum_{k=0}^n 2^{-k} = \frac{2^{n+1}-1}{2^n}$

Proof by induction of summation inequality: $1 + 1/2+ 1/3+ 1/4+1/5+⋯+ 1/2^n \leq n + 1$

Prove $\left(1-\frac{1}{n^2}\right)^n\times\left(1+\frac 1n\right)<1$ for every natural $n > 0$ by induction

Inductive Proof With Regular Expression

Mathematical Proof By Induction of $1 + 2 +\dots + n = (n + 1)n/2$

Is induction something we take on faith?

Connectivity in a graph with even-degree vertices is preserved by edge removal

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