List questions from induction

Published on 08 Apr 2014 - 8:31

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For $f: \mathbb{R}^n \to \mathbb{R}$ homogenous, show that $\sum_{i=1}^n x_i \frac{\partial f}{\partial x_i}(x_1, \dots ,x_n)= kf(x_1, \dots , x_n)$

Published on 29 Mar 2026 - 19:30

175

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Show that this summation is an invariant of the loop in algorithm

Published on 08 Apr 2014 - 23:02

926

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Use Bonnet recursion formula to prove by induction

Published on 25 Mar 2026 - 8:07

215

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Inductive proof about Jensen's inequality

Published on 09 Apr 2014 - 3:42

112

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Probability of a Union of Events

Published on 10 Apr 2014 - 3:36

119

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Solving the LaPlace PDE by complete induction

Published on 29 Mar 2026 - 21:22

47

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Recursion, Explicit Equasion

Published on 27 Mar 2026 - 21:43

540

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Proof of definite integral $\int_0^{\pi/2} \frac{\sin(2n+1)x}{\sin x}dx=\frac\pi2$ using induction

Published on 11 Apr 2014 - 8:23

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Finding the formula for the sum of a the sequence $1 + 4 + 7 + ... + (3n + 1)$

Published on 26 Mar 2026 - 13:02

772

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Proof by Induction Algorithm

Published on 12 Apr 2014 - 8:46

56

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Where did this "+1" term come from for this inductive proof?

Published on 13 Apr 2014 - 2:13

312

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How does mutual induction work?

Published on 13 Apr 2014 - 2:20

72

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Induction proof that $4^n > 3^n+2^n$ for $n\ge2$

Published on 13 Apr 2014 - 3:18

143

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How to use induction on this type of inequality?

Published on 13 Apr 2014 - 19:49

List Question

Proof by induction for divisibility by power of 2^n

For $f: \mathbb{R}^n \to \mathbb{R}$ homogenous, show that $\sum_{i=1}^n x_i \frac{\partial f}{\partial x_i}(x_1, \dots ,x_n)= kf(x_1, \dots , x_n)$

Show that this summation is an invariant of the loop in algorithm

Use Bonnet recursion formula to prove by induction

Inductive proof about Jensen's inequality

Probability of a Union of Events

Solving the LaPlace PDE by complete induction

Recursion, Explicit Equasion

Proof of definite integral $\int_0^{\pi/2} \frac{\sin(2n+1)x}{\sin x}dx=\frac\pi2$ using induction

Finding the formula for the sum of a the sequence $1 + 4 + 7 + ... + (3n + 1)$

Proof by Induction Algorithm

Where did this "+1" term come from for this inductive proof?

How does mutual induction work?

Induction proof that $4^n > 3^n+2^n$ for $n\ge2$

How to use induction on this type of inequality?

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