Question

Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$

score 1.8k · Answer 1 · 2014-06-10 19:23:40

1.8k

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Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$

Published on 10 Jun 2014 - 19:23

score 948 · Answer 2 · 2014-06-11 07:55:28

948

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induction proof of recursive multiplication

Published on 11 Jun 2014 - 7:55

score 154 · Answer 3 · 2014-06-11 21:37:11

Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$

score 135 · Answer 4 · 2014-06-12 06:58:05

135

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Why does one modulus disappear when modded by another modulus?

Published on 12 Jun 2014 - 6:58

score 311 · Answer 5 · 2014-06-12 09:13:32

311

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Prove by induction that $(n+1)^2 + (n+2)^2 + ... + (2n)^2 = \frac{n(2n+1)(7n+1)}{6}$

Published on 12 Jun 2014 - 9:13

score 549 · Answer 6 · 2014-06-13 04:19:40

549

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Proving Hermite's identity using induction

Published on 13 Jun 2014 - 4:19

score 320 · Answer 7 · 2014-06-13 11:10:32

320

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Proof by induction that $(1^3 + 2^3 + 3^3+\cdots+n^3) = (1 + 2 + \cdots + n)^2$

Published on 13 Jun 2014 - 11:10

score 2.5k · Answer 8 · 2014-06-14 10:06:42

2.5k

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Complete induction proof that every $n > 1$ can be written as a product of primes

Published on 14 Jun 2014 - 10:06

score 1.2k · Answer 9 · 2026-03-26 06:22:34

1.2k

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How to prove by induction the constructibility of a line segment of length $\sqrt{n}$?

Published on 26 Mar 2026 - 6:22

score 3.1k · Answer 10 · 2026-03-26 06:03:00

3.1k

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How to prove a very basic algorithm by induction

Published on 26 Mar 2026 - 6:03

score 304 · Answer 11 · 2014-06-14 18:25:45

304

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Finding a proof to the 'squares' problem

Published on 14 Jun 2014 - 18:25

score 119 · Answer 12 · 2014-06-15 23:01:34

119

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Prove by induction $n^{n+1}>(n+1)^{n}$, for $n\geq3$

Published on 15 Jun 2014 - 23:01

score 136 · Answer 13 · 2014-06-16 00:51:54

136

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Use induction to show that $a_{n+1}-a_n=\biggl(-\frac{1}{2} \biggr)^n (a_1-a_0) .$

Published on 16 Jun 2014 - 0:51

score 246 · Answer 14 · 2014-06-16 03:34:42

246

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Problems relating to fibonacci sequence via induction

Published on 16 Jun 2014 - 3:34

score 289 · Answer 15 · 2014-06-20 18:25:25

289

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Generalized Induction Verification

Published on 20 Jun 2014 - 18:25

List Question

Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$

induction proof of recursive multiplication

Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$

Why does one modulus disappear when modded by another modulus?

Prove by induction that $(n+1)^2 + (n+2)^2 + ... + (2n)^2 = \frac{n(2n+1)(7n+1)}{6}$

Proving Hermite's identity using induction

Proof by induction that $(1^3 + 2^3 + 3^3+\cdots+n^3) = (1 + 2 + \cdots + n)^2$

Complete induction proof that every $n > 1$ can be written as a product of primes

How to prove by induction the constructibility of a line segment of length $\sqrt{n}$?

How to prove a very basic algorithm by induction

Finding a proof to the 'squares' problem

Prove by induction $n^{n+1}>(n+1)^{n}$, for $n\geq3$

Use induction to show that $a_{n+1}-a_n=\biggl(-\frac{1}{2} \biggr)^n (a_1-a_0) .$

Problems relating to fibonacci sequence via induction

Generalized Induction Verification

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