Question

How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?

score 522 · Answer 1 · 2016-07-25 13:28:09

522

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How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?

Published on 25 Jul 2016 - 13:28

score 749 · Answer 2 · 2026-04-11 21:37:33

749

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Are there any proofs that only exist by induction?

Published on 11 Apr 2026 - 21:37

score 278 · Answer 3 · 2026-04-11 21:17:39

278

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How to prove inequality $3^{n}≤4n!$ for $n≥4$ with mathematical induction?

Published on 11 Apr 2026 - 21:17

score 55 · Answer 4 · 2026-04-10 20:42:52

55

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Choosing values in a strong induction

Published on 10 Apr 2026 - 20:42

score 5.7k · Answer 5 · 2026-04-12 14:14:44

5.7k

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Induction - Countable Union of Countable Sets

Published on 12 Apr 2026 - 14:14

score 375 · Answer 6 · 2026-04-12 03:22:17

375

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Bernoulli inequality application

Published on 12 Apr 2026 - 3:22

score 1.3k · Answer 7 · 2026-03-25 19:07:13

1.3k

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Can we say that $\prod_{i=1}^n (1-x_i)\ge 1-\sum_{i=1}^n x_i,\ \forall n\in \mathbb{N},\ \forall x_i\in [0,1)$?

Published on 25 Mar 2026 - 19:07

score 170 · Answer 8 · 2026-04-09 17:34:03

170

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Prove using induction the following equation is true.

Published on 09 Apr 2026 - 17:34

score 189 · Answer 9 · 2016-07-27 23:38:53

189

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What's the shortest way to prove $\sum_{t=1}^n t^2=\frac{n(n+1)(2n+1)}6$ by a mathematical induction?

Published on 27 Jul 2016 - 23:38

score 633 · Answer 10 · 2026-04-10 13:31:56

633

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How does the induction axiom rule out numbers other than the naturals?

Published on 10 Apr 2026 - 13:31

score 215 · Answer 11 · 2026-03-30 18:09:46

215

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Prove $2^n \lt\ n!$

Published on 30 Mar 2026 - 18:09

score 177 · Answer 12 · 2026-04-10 21:57:06

177

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Can Robinson's Axiom be used to prove mathematical induction?

Published on 10 Apr 2026 - 21:57

score 189 · Answer 13 · 2026-04-12 17:12:21

189

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how can I prove this $\sum_{k=1}^{n}\frac{1}{4k^{2}-2k}=\sum_{k=n+1}^{2n}\frac{1}{k}$

Published on 12 Apr 2026 - 17:12

score 87 · Answer 14 · 2016-07-31 20:31:31

87

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Prove that $\prod_{k=0}^{n-1}(1+x^{2^k})=\sum_{j=0}^{2^n-1}x^j$

Published on 31 Jul 2016 - 20:31

score 517 · Answer 15 · 2026-04-10 05:27:05

517

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How can know if a proof technique can actually prove something? Specifically, induction

Published on 10 Apr 2026 - 5:27

List Question

How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?

Are there any proofs that only exist by induction?

How to prove inequality $3^{n}≤4n!$ for $n≥4$ with mathematical induction?

Choosing values in a strong induction

Induction - Countable Union of Countable Sets

Bernoulli inequality application

Can we say that $\prod_{i=1}^n (1-x_i)\ge 1-\sum_{i=1}^n x_i,\ \forall n\in \mathbb{N},\ \forall x_i\in [0,1)$?

Prove using induction the following equation is true.

What's the shortest way to prove $\sum_{t=1}^n t^2=\frac{n(n+1)(2n+1)}6$ by a mathematical induction?

How does the induction axiom rule out numbers other than the naturals?

Prove $2^n \lt\ n!$

Can Robinson's Axiom be used to prove mathematical induction?

how can I prove this $\sum_{k=1}^{n}\frac{1}{4k^{2}-2k}=\sum_{k=n+1}^{2n}\frac{1}{k}$

Prove that $\prod_{k=0}^{n-1}(1+x^{2^k})=\sum_{j=0}^{2^n-1}x^j$

How can know if a proof technique can actually prove something? Specifically, induction

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