Question

Show that $n!<n^n $ where $n>1$ and is a Positive Integer

score 75 · Answer 1 · 2014-12-01 19:12:53

75

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Show that $n!<n^n $ where $n>1$ and is a Positive Integer

Published on 01 Dec 2014 - 19:12

score 231 · Answer 2 · 2014-12-01 20:17:53

231

Views

Prove $1 + \frac{1}{4} + \frac{1}{9} + \cdots + \frac{1}{n^2} < 2 - \frac{1}{n}$ by Induction

Published on 01 Dec 2014 - 20:17

score 87 · Answer 3 · 2014-12-01 21:52:02

87

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Use mathematical induction to prove $\sum_{i=1}^{n}(2i+4)=n^2+5n$

Published on 01 Dec 2014 - 21:52

score 163 · Answer 4 · 2026-03-27 00:00:20

163

Views

Proof by induction, or without it if possible?

Published on 27 Mar 2026 - 0:00

score 141 · Answer 5 · 2014-12-03 16:58:22

141

Views

Show: $\left(\sum_{k=0}^n a_k\right)^2\leqslant (n+1)\sum_{k=0}^n a_k^2$

Published on 03 Dec 2014 - 16:58

score 97 · Answer 6 · 2026-03-25 19:05:41

97

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Proof by induction of the formula for $2^0+2^1+2^2+...+2^n$?

Published on 25 Mar 2026 - 19:05

score 50.6k · Answer 7 · 2026-03-26 21:26:25

50.6k

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Prove that $1 + 4 + 7 + · · · + 3n − 2 = \frac {n(3n − 1)}{2}$

Published on 26 Mar 2026 - 21:26

score 51 · Answer 8 · 2014-12-04 13:17:31

51

Views

Using mathematical induction on natural numbers to show ∀n. 0+2+4+...+2·n = n·(n+1)

Published on 04 Dec 2014 - 13:17

score 138 · Answer 9 · 2014-12-04 15:44:32

138

Views

Show that $\prod_{i=2}^n \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$for $n \in \Bbb{N}$, $ n \ge 2$

Published on 04 Dec 2014 - 15:44

score 114 · Answer 10 · 2026-03-30 05:32:16

114

Views

Concise induction step for proving $\sum_{i=1}^n i^3 = \left( \sum_{i=1}^ni\right)^2$

Published on 30 Mar 2026 - 5:32

score 77 · Answer 11 · 2026-04-05 23:09:04

77

Views

Proof by induction that if $a_0 = 1$ and $a_n = n + 2 a_{n-1}$, then $a_n \ge 2^n + n^2$.

Published on 05 Apr 2026 - 23:09

score 322 · Answer 12 · 2014-12-05 19:17:42

322

Views

Error in induction proof

Published on 05 Dec 2014 - 19:17

score 61 · Answer 13 · 2014-12-05 19:32:37

61

Views

Proof by induction, is my proof incorrect?

Published on 05 Dec 2014 - 19:32

score 2.5k · Answer 14 · 2026-03-26 16:04:07

2.5k

Views

how to point out errors in proof by induction

Published on 26 Mar 2026 - 16:04

score 14.1k · Answer 15 · 2014-12-06 16:45:27

14.1k

Views

number of edges induction proof

Published on 06 Dec 2014 - 16:45

List Question

Show that $n!<n^n $ where $n>1$ and is a Positive Integer

Prove $1 + \frac{1}{4} + \frac{1}{9} + \cdots + \frac{1}{n^2} < 2 - \frac{1}{n}$ by Induction

Use mathematical induction to prove $\sum_{i=1}^{n}(2i+4)=n^2+5n$

Proof by induction, or without it if possible?

Show: $\left(\sum_{k=0}^n a_k\right)^2\leqslant (n+1)\sum_{k=0}^n a_k^2$

Proof by induction of the formula for $2^0+2^1+2^2+...+2^n$?

Prove that $1 + 4 + 7 + · · · + 3n − 2 = \frac {n(3n − 1)}{2}$

Using mathematical induction on natural numbers to show ∀n. 0+2+4+...+2·n = n·(n+1)

Show that $\prod_{i=2}^n \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$for $n \in \Bbb{N}$, $ n \ge 2$

Concise induction step for proving $\sum_{i=1}^n i^3 = \left( \sum_{i=1}^ni\right)^2$

Proof by induction that if $a_0 = 1$ and $a_n = n + 2 a_{n-1}$, then $a_n \ge 2^n + n^2$.

Error in induction proof

Proof by induction, is my proof incorrect?

how to point out errors in proof by induction

number of edges induction proof

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