Question

How can I prove through mathematical induction that $(n!)^{(1/n)}\le(n+1)/2$?

score 82 · Answer 1 · 2019-11-24 13:22:23

82

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How can I prove through mathematical induction that $(n!)^{(1/n)}\le(n+1)/2$?

Published on 24 Nov 2019 - 13:22

score 702 · Answer 2 · 2026-03-28 03:03:07

702

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Structural Induction: Prove that all ternary trees with $n$ vertices have a height of at least $\lfloor\log_{3}{n}\rfloor$

Published on 28 Mar 2026 - 3:03

score 123 · Answer 3 · 2019-11-25 01:45:51

123

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Show that $S$ is a convex set, if it is locally convex everywhere

Published on 25 Nov 2019 - 1:45

score 74 · Answer 4 · 2019-11-25 06:36:31

74

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Incomprehensible induction from Johnsonbaugh's book.

Published on 25 Nov 2019 - 6:36

score 145 · Answer 5 · 2019-11-25 11:39:23

145

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I need help proving an inequality by induction

Published on 25 Nov 2019 - 11:39

score 53 · Answer 6 · 2019-11-25 19:18:13

53

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Show $\phi_j(x)=\frac{\phi_{j-1}(x)-\phi_{j-1}(0)}{x}$ for $\phi_j(x):=\frac{1}{(j-1)!}\int_{0}^{1}e^{(1-\theta)x}\theta^{j-1}d\theta$

Published on 25 Nov 2019 - 19:18

score 361 · Answer 7 · 2026-03-29 14:57:17

361

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Alternative Proof for ${n\choose k}$ is integer

Published on 29 Mar 2026 - 14:57

score 219 · Answer 8 · 2026-03-27 10:45:50

219

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Proving the number of steps in Merge Sort algorithm based on a recurrence

Published on 27 Mar 2026 - 10:45

score 60 · Answer 9 · 2019-11-28 07:31:22

60

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Why is this Induction Proof Wrong?

Published on 28 Nov 2019 - 7:31

score 284 · Answer 10 · 2019-11-28 18:29:31

284

Views

Find the largest score a rugby team cannot get exactly using just 3-point field goals and 7-point tries.

Published on 28 Nov 2019 - 18:29

score 53 · Answer 11 · 2019-11-28 19:12:28

53

Views

Prove by induction this inequality

Published on 28 Nov 2019 - 19:12

score 77 · Answer 12 · 2019-11-28 21:56:39

77

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Descending induction variant(s)

Published on 28 Nov 2019 - 21:56

score 82 · Answer 13 · 2019-11-29 12:55:27

82

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Show that the sequence $(an)_{n \in \mathbb N}$ is increasing using induction.

Published on 29 Nov 2019 - 12:55

score 98 · Answer 14 · 2026-04-06 20:37:53

98

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binomial identities

Published on 06 Apr 2026 - 20:37

score 1.6k · Answer 15 · 2026-03-29 14:57:52

1.6k

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Prove by mathematical induction that $n! < n^n$ where $n > 1$

Published on 29 Mar 2026 - 14:57

List Question

How can I prove through mathematical induction that $(n!)^{(1/n)}\le(n+1)/2$?

Structural Induction: Prove that all ternary trees with $n$ vertices have a height of at least $\lfloor\log_{3}{n}\rfloor$

Show that $S$ is a convex set, if it is locally convex everywhere

Incomprehensible induction from Johnsonbaugh's book.

I need help proving an inequality by induction

Show $\phi_j(x)=\frac{\phi_{j-1}(x)-\phi_{j-1}(0)}{x}$ for $\phi_j(x):=\frac{1}{(j-1)!}\int_{0}^{1}e^{(1-\theta)x}\theta^{j-1}d\theta$

Alternative Proof for ${n\choose k}$ is integer

Proving the number of steps in Merge Sort algorithm based on a recurrence

Why is this Induction Proof Wrong?

Find the largest score a rugby team cannot get exactly using just 3-point field goals and 7-point tries.

Prove by induction this inequality

Descending induction variant(s)

Show that the sequence $(an)_{n \in \mathbb N}$ is increasing using induction.

binomial identities

Prove by mathematical induction that $n! < n^n$ where $n > 1$

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