Question

Induction. Prove: $n! \ge 3^{n-1}/2$ for $n\geq1$

score 71 · Answer 1 · 2018-07-04 23:17:50

71

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Induction. Prove: $n! \ge 3^{n-1}/2$ for $n\geq1$

Published on 04 Jul 2018 - 23:17

score 1.7k · Answer 2 · 2026-03-26 01:35:00

1.7k

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Prove by induction: $3^n+1$ is divisible by $2$ for $n\ge 0$

Published on 26 Mar 2026 - 1:35

score 158 · Answer 3 · 2026-03-26 22:12:43

158

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Additive number theory clarification

Published on 26 Mar 2026 - 22:12

score 516 · Answer 4 · 2018-07-09 12:38:44

516

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Prove by induction $\sum_{i=1}^n 3i(i+4) = \frac{(n)(n+1)(2n+13)}{2}$

Published on 09 Jul 2018 - 12:38

score 1k · Answer 5 · 2018-07-10 09:10:32

1k

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Prove by induction $\sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}$

Published on 10 Jul 2018 - 9:10

score 97 · Answer 6 · 2018-07-10 10:35:15

97

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Prove by induction $\sum_{i=1}^n i\cdot 2^{i-1} =(n-1)\cdot 2^n+1$

Published on 10 Jul 2018 - 10:35

score 94 · Answer 7 · 2026-03-25 12:33:50

94

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Double induction on ordinals (If $\ \alpha+1=\beta+1$ then $\alpha=\beta$)

Published on 25 Mar 2026 - 12:33

score 185 · Answer 8 · 2018-07-10 20:14:13

185

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Kleene "Introduction to Metamathematics" problem on parentheses

Published on 10 Jul 2018 - 20:14

score 314 · Answer 9 · 2018-07-11 22:22:32

314

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Proof by Induction: If $x_1x_2\dots x_n=1$ then $x_1 + x_2 + \dots + x_n\ge n$

Published on 11 Jul 2018 - 22:22

score 71 · Answer 10 · 2018-07-13 03:03:50

71

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Significance of $1 + 2 + 3 . . . +2n$ within inductive proof

Published on 13 Jul 2018 - 3:03

score 796 · Answer 11 · 2026-03-25 04:37:59

796

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Does countable induction over $\mathbb N$ require the axiom of infinity?

Published on 25 Mar 2026 - 4:37

score 156 · Answer 12 · 2026-03-25 12:54:31

156

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In a mathematical induction, can you prove the "n'th case implies n+1'th case" step by contrapositive?

Published on 25 Mar 2026 - 12:54

score 154 · Answer 13 · 2026-03-25 14:39:20

154

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How to derive the formula to compute an integer window number for given window width and overlap fraction (example given)

Published on 25 Mar 2026 - 14:39

score 3.4k · Answer 14 · 2018-07-19 03:20:53

3.4k

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Proving convergence of geometric series by induction

Published on 19 Jul 2018 - 3:20

score 577 · Answer 15 · 2026-03-22 17:49:14

577

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Contents of Gentzen's consistency proof of PA

Published on 22 Mar 2026 - 17:49

List Question

Induction. Prove: $n! \ge 3^{n-1}/2$ for $n\geq1$

Prove by induction: $3^n+1$ is divisible by $2$ for $n\ge 0$

Additive number theory clarification

Prove by induction $\sum_{i=1}^n 3i(i+4) = \frac{(n)(n+1)(2n+13)}{2}$

Prove by induction $\sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}$

Prove by induction $\sum_{i=1}^n i\cdot 2^{i-1} =(n-1)\cdot 2^n+1$

Double induction on ordinals (If $\ \alpha+1=\beta+1$ then $\alpha=\beta$)

Kleene "Introduction to Metamathematics" problem on parentheses

Proof by Induction: If $x_1x_2\dots x_n=1$ then $x_1 + x_2 + \dots + x_n\ge n$

Significance of $1 + 2 + 3 . . . +2n$ within inductive proof

Does countable induction over $\mathbb N$ require the axiom of infinity?

In a mathematical induction, can you prove the "n'th case implies n+1'th case" step by contrapositive?

How to derive the formula to compute an integer window number for given window width and overlap fraction (example given)

Proving convergence of geometric series by induction

Contents of Gentzen's consistency proof of PA

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