Question

How do I prove by mathematical induction that $n!<n^{n-1}$ where $n\geq3$? Did I do it right?

score 50 · Answer 1 · 2014-11-05 14:58:43

50

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How do I prove by mathematical induction that $n!<n^{n-1}$ where $n\geq3$? Did I do it right?

Published on 05 Nov 2014 - 14:58

score 7.1k · Answer 2 · 2014-11-05 22:03:07

7.1k

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Using Induction to prove complete binary trees

Published on 05 Nov 2014 - 22:03

score 63 · Answer 3 · 2014-11-06 07:29:42

63

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Prove if $a_{1},...,a_{n}$ are elements of a group $G$, then $(a_{1}a_{2}...a{_n})^{-1}=((a_{1})^{-1})...*((a_{n})^{-1})$

Published on 06 Nov 2014 - 7:29

score 2.6k · Answer 4 · 2014-11-06 13:58:55

2.6k

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Proof of 3-chain subsequence problem from assignment 2 of MIT OCW 6.042

Published on 06 Nov 2014 - 13:58

score 287 · Answer 5 · 2014-11-06 18:43:32

287

Views

proof by mathematical induction with the summation operator?

Published on 06 Nov 2014 - 18:43

score 476 · Answer 6 · 2014-11-07 20:07:59

476

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proving that $(n-1)^n>n^{n-1}$

Published on 07 Nov 2014 - 20:07

score 912 · Answer 7 · 2026-03-27 04:34:26

912

Views

Proof of Euler's Totient Theorem

Published on 27 Mar 2026 - 4:34

score 958 · Answer 8 · 2014-11-08 10:16:06

958

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Finding the fake coin from $3^n$ coins by weighing (proving by induction)

Published on 08 Nov 2014 - 10:16

score 257 · Answer 9 · 2026-03-25 14:25:11

257

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Show that $-2, -1, 0, i$ lies in the Mandelbrot set but that $1$ lies outside of it

Published on 25 Mar 2026 - 14:25

score 137 · Answer 10 · 2014-11-08 19:35:55

137

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How to prove $ 1^3+2^3+... +n^3 = (1 + 2+ \dots +n)^2 $ by induction?

Published on 08 Nov 2014 - 19:35

score 580 · Answer 11 · 2026-04-01 15:59:35

580

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The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.

Published on 01 Apr 2026 - 15:59

score 96 · Answer 12 · 2014-11-09 04:36:09

96

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Is there a proof of $\sum_{n=0}^x {{(-1)^n(x-n+1)^x}\over{n!(x-n)!}} = 1$ using induction?

Published on 09 Nov 2014 - 4:36

score 101 · Answer 13 · 2026-03-27 04:38:50

101

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Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

Published on 27 Mar 2026 - 4:38

score 43 · Answer 14 · 2014-11-09 17:00:36

43

Views

Help with Mathematical Induction

Published on 09 Nov 2014 - 17:00

score 88 · Answer 15 · 2014-11-09 20:18:00

88

Views

General form of iterates $f^{n}(x)$ for $f(x) = \frac{x}{1-x}$

Published on 09 Nov 2014 - 20:18

List Question

How do I prove by mathematical induction that $n!<n^{n-1}$ where $n\geq3$? Did I do it right?

Using Induction to prove complete binary trees

Prove if $a_{1},...,a_{n}$ are elements of a group $G$, then $(a_{1}a_{2}...a{_n})^{-1}=((a_{1})^{-1})...*((a_{n})^{-1})$

Proof of 3-chain subsequence problem from assignment 2 of MIT OCW 6.042

proof by mathematical induction with the summation operator?

proving that $(n-1)^n>n^{n-1}$

Proof of Euler's Totient Theorem

Finding the fake coin from $3^n$ coins by weighing (proving by induction)

Show that $-2, -1, 0, i$ lies in the Mandelbrot set but that $1$ lies outside of it

How to prove $ 1^3+2^3+... +n^3 = (1 + 2+ \dots +n)^2 $ by induction?

The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.

Is there a proof of $\sum_{n=0}^x {{(-1)^n(x-n+1)^x}\over{n!(x-n)!}} = 1$ using induction?

Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

Help with Mathematical Induction

General form of iterates $f^{n}(x)$ for $f(x) = \frac{x}{1-x}$

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