List questions from induction

Published on 14 Apr 2026 - 0:26

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Recurrence relationship

Published on 04 May 2026 - 16:58

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Prove by induction: $\sum\limits_{k=1}^{n}\frac{1}{2^k}\tan\frac{x}{2^k}=\frac{1}{2^n}\cot\frac{x}{2^n}-\cot x,x\neq k\pi,k\in \mathbb{Z}$

Published on 16 Apr 2026 - 13:04

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Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$

Published on 16 Apr 2026 - 3:31

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how to solve this induction problem?

Published on 09 Apr 2026 - 7:29

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Is this proof of the worst-case performance of linear search correct?

Published on 04 Apr 2026 - 5:03

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Prove by induction: $\sum\limits_{k=1}^{n}(-1)^{k+1}{n\choose k}\frac{1}{k}=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$

Published on 16 Apr 2026 - 13:04

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Induction proof of exponential and factorial inequality

Published on 03 Apr 2026 - 23:06

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Prove: $\frac{(2n)!}{n!(n+1)!}\in \mathbb{N}, \forall n\in\mathbb{N}$

Published on 14 Apr 2026 - 18:05

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2^m marbles in multiple boxes.

Published on 18 Oct 2015 - 4:53

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Flipping bits and crossing strings induction problem.

Published on 10 Apr 2026 - 10:50

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Upper estimate for partial sums of the series $\sum 1/n^3$

Published on 15 Apr 2026 - 15:22

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proof that $n^2 + 2n \leq 5^n $

Published on 14 Apr 2026 - 3:47

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Proving a mangled graph to be connected.

Published on 27 Apr 2026 - 3:20

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Question regarding proof by Induction

Published on 13 Apr 2026 - 23:31

List Question

Basic Induction

Recurrence relationship

Prove by induction: $\sum\limits_{k=1}^{n}\frac{1}{2^k}\tan\frac{x}{2^k}=\frac{1}{2^n}\cot\frac{x}{2^n}-\cot x,x\neq k\pi,k\in \mathbb{Z}$

Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$

how to solve this induction problem?

Is this proof of the worst-case performance of linear search correct?

Prove by induction: $\sum\limits_{k=1}^{n}(-1)^{k+1}{n\choose k}\frac{1}{k}=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$

Induction proof of exponential and factorial inequality

Prove: $\frac{(2n)!}{n!(n+1)!}\in \mathbb{N}, \forall n\in\mathbb{N}$

2^m marbles in multiple boxes.

Flipping bits and crossing strings induction problem.

Upper estimate for partial sums of the series $\sum 1/n^3$

proof that $n^2 + 2n \leq 5^n $

Proving a mangled graph to be connected.

Question regarding proof by Induction

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