Question

Show by induction that $F_n \geq 2^{0.5 \cdot n}$, for $n \geq 6$

score 3.9k · Answer 1 · 2026-04-17 06:25:25

3.9k

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Show by induction that $F_n \geq 2^{0.5 \cdot n}$, for $n \geq 6$

Published on 17 Apr 2026 - 6:25

score 81 · Answer 2 · 2026-04-17 06:29:26

81

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Showing that $\frac{1}{2^n +1} + \frac{1}{2^n +2} + \cdots + \frac{1}{2^{n+1}}\geq \frac{1}{2}$ for all $n\geq 1$

Published on 17 Apr 2026 - 6:29

score 290 · Answer 3 · 2026-04-15 23:32:08

290

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Prove that “No one likes Reggae music” is the same as “Everyone does not like Reggae music”.

Published on 15 Apr 2026 - 23:32

score 150 · Answer 4 · 2026-04-17 04:27:48

150

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Prove by induction: $\frac{1}{2!}+\frac{2}{3!}+\cdots+\frac{n}{(n+1)!}=\frac{n!-1}{n!}$

Published on 17 Apr 2026 - 4:27

score 3.3k · Answer 5 · 2026-04-14 01:06:54

3.3k

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People sitting in a circle chewing gum

Published on 14 Apr 2026 - 1:06

score 83 · Answer 6 · 2026-04-16 08:47:45

83

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Is this proof by induction that $|\Bbb Q^n|=\aleph_0$ correct?

Published on 16 Apr 2026 - 8:47

score 657 · Answer 7 · 2026-04-16 17:18:10

657

Views

Proving $\sum_{j=1}^n \frac{1}{\sqrt{j}} > \sqrt{n}$ with induction

Published on 16 Apr 2026 - 17:18

score 283 · Answer 8 · 2026-04-14 09:30:45

283

Views

Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$

Published on 14 Apr 2026 - 9:30

score 170 · Answer 9 · 2026-04-16 22:39:15

170

Views

Prove $1^3+2^3+...+n^3 = (1+2+...+n)^2$ for all positive integers $n$.

Published on 16 Apr 2026 - 22:39

score 602 · Answer 10 · 2026-04-16 21:06:10

602

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Proving that $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{2n-1}-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}$

Published on 16 Apr 2026 - 21:06

score 76 · Answer 11 · 2026-04-10 19:34:23

76

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Understanding a step in this proof by induction

Published on 10 Apr 2026 - 19:34

score 7.4k · Answer 12 · 2026-04-18 15:04:22

7.4k

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Prove that sequence $a_1 = \sqrt{2}$, $a_{n+1} = \sqrt{2 + a_n}$ is bounded above by 3

Published on 18 Apr 2026 - 15:04

score 70 · Answer 13 · 2026-04-17 05:16:02

70

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Check my solution: For the recurrence $a_{n+3}=a_{n+2}+a_{n+1}+a_n$ where $a_1=a_2=a_3=1$, prove that $a_n\leq 2^{n-2}$.

Published on 17 Apr 2026 - 5:16

score 163 · Answer 14 · 2026-04-15 16:12:00

I have to prove by mathematical induction that $\frac{(2n)!}{n!(n+1) !}$ is a natural number for all $n\in\mathbb{N}$.

score 989 · Answer 15 · 2026-04-11 18:47:44

989

Views

Uses of "Collatz induction"?

Published on 11 Apr 2026 - 18:47

List Question

Show by induction that $F_n \geq 2^{0.5 \cdot n}$, for $n \geq 6$

Showing that $\frac{1}{2^n +1} + \frac{1}{2^n +2} + \cdots + \frac{1}{2^{n+1}}\geq \frac{1}{2}$ for all $n\geq 1$

Prove that “No one likes Reggae music” is the same as “Everyone does not like Reggae music”.

Prove by induction: $\frac{1}{2!}+\frac{2}{3!}+\cdots+\frac{n}{(n+1)!}=\frac{n!-1}{n!}$

People sitting in a circle chewing gum

Is this proof by induction that $|\Bbb Q^n|=\aleph_0$ correct?

Proving $\sum_{j=1}^n \frac{1}{\sqrt{j}} > \sqrt{n}$ with induction

Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$

Prove $1^3+2^3+...+n^3 = (1+2+...+n)^2$ for all positive integers $n$.

Proving that $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{2n-1}-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}$

Understanding a step in this proof by induction

Prove that sequence $a_1 = \sqrt{2}$, $a_{n+1} = \sqrt{2 + a_n}$ is bounded above by 3

Check my solution: For the recurrence $a_{n+3}=a_{n+2}+a_{n+1}+a_n$ where $a_1=a_2=a_3=1$, prove that $a_n\leq 2^{n-2}$.

I have to prove by mathematical induction that $\frac{(2n)!}{n!(n+1) !}$ is a natural number for all $n\in\mathbb{N}$.

Uses of "Collatz induction"?

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