List questions from induction

Published on 21 May 2019 - 16:34

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Prove by induction that, for all $n\in\Bbb N$, $\sqrt{n} ≤ \sum_ {k=1}^n \frac{1}{\sqrt{k}} < \sqrt{n} + \frac{n}{\sqrt{n+1}}$.

Published on 22 May 2019 - 3:42

632

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How to show that $(n!/n^n)_{n\geq 0}$ is a null sequence?

Published on 22 May 2019 - 21:11

354

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What is a good example of prefix induction?

Published on 29 Mar 2026 - 10:15

47

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Property takagi function by induction.

Published on 23 May 2019 - 10:24

120

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Two dimensional induction

Published on 23 May 2019 - 16:08

175

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Strong induction

Published on 23 May 2019 - 17:19

382

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Proving the number of internal nodes of a binary tree

Published on 26 Mar 2026 - 16:05

670

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Principle of mathematical induction, negative numbers

Published on 24 May 2019 - 1:48

69

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Telescoping Rhombuses

Published on 24 May 2019 - 2:34

277

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Wikipedia's proof of Jensen's inequality

Published on 25 Mar 2026 - 8:09

74

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How to prove $n^{3/2} \le 2^n/n$ for all $n\geq 8$ via Induction?

Published on 24 May 2019 - 17:10

349

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Discrete mathematics - understanding proof by induction

Published on 27 Mar 2026 - 6:51

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Show that $A_1,...,A_n\vDash_{taut} B \leftrightarrow \vDash_{taut} A_1 \to A_2\to ...\to A_n\to B$

Published on 26 May 2019 - 20:07

106

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What is actually proved in this exclusion of infinite decimal expressions of the form $a_0.a_1 a_2\dots _\bar{9}$?

Published on 27 May 2019 - 21:46

List Question

Prove $5^n + 3^n - 2^{2n+1} > 0$ by induction

Prove by induction that, for all $n\in\Bbb N$, $\sqrt{n} ≤ \sum_ {k=1}^n \frac{1}{\sqrt{k}} < \sqrt{n} + \frac{n}{\sqrt{n+1}}$.

How to show that $(n!/n^n)_{n\geq 0}$ is a null sequence?

What is a good example of prefix induction?

Property takagi function by induction.

Two dimensional induction

Strong induction

Proving the number of internal nodes of a binary tree

Principle of mathematical induction, negative numbers

Telescoping Rhombuses

Wikipedia's proof of Jensen's inequality

How to prove $n^{3/2} \le 2^n/n$ for all $n\geq 8$ via Induction?

Discrete mathematics - understanding proof by induction

Show that $A_1,...,A_n\vDash_{taut} B \leftrightarrow \vDash_{taut} A_1 \to A_2\to ...\to A_n\to B$

What is actually proved in this exclusion of infinite decimal expressions of the form $a_0.a_1 a_2\dots _\bar{9}$?

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