Question

Use Mathematical Induction to prove that for all integers $n\geq 5, 1+4n<2^n$

score 668 · Answer 1 · 2020-04-22 01:08:30

668

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Use Mathematical Induction to prove that for all integers $n\geq 5, 1+4n<2^n$

Published on 22 Apr 2020 - 1:08

score 215 · Answer 2 · 2020-04-22 09:59:50

Prove by induction $u_{n+2}+u_n=4u_{n+1}$ for all $n\in \mathbb{N}$, where $u_n=(2+\sqrt{3})^n+(2-\sqrt{3})^n$.

score 45 · Answer 3 · 2026-04-09 05:33:14

45

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Sylvester matrix column orthogonality

Published on 09 Apr 2026 - 5:33

score 446 · Answer 4 · 2026-04-11 10:30:09

446

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Proof by induction of number of edges in complete (fully connected) graph

Published on 11 Apr 2026 - 10:30

score 162 · Answer 5 · 2020-04-22 20:22:37

162

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Induction based on the 2-cocycle identity for $c': \Bbb Z/p \times \Bbb Z/p \to \Bbb Z/p$ and $c'(0, 0) = 0$

Published on 22 Apr 2020 - 20:22

score 51 · Answer 6 · 2026-03-30 11:37:49

51

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Proving $\frac{b-a}{b-x}\cdot (\frac{b-a}{k+1})^{k+1}\geq (\frac{b-a}{k})^{k+1}$

Published on 30 Mar 2026 - 11:37

score 44 · Answer 7 · 2020-04-23 19:42:06

44

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Proving $1 + 2 + 2^2+2^3 + 2^4 + \dots+ 2^{n-1}= 2^n -1$ using mathematical induction

Published on 23 Apr 2020 - 19:42

score 50 · Answer 8 · 2026-04-10 14:41:57

50

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Questions about induction and Big O

Published on 10 Apr 2026 - 14:41

score 32 · Answer 9 · 2020-04-24 06:49:21

32

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Prove the following statements about the geometric sum.

Published on 24 Apr 2020 - 6:49

score 67 · Answer 10 · 2020-04-25 17:14:43

67

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beginner with induction, something I don't understand

Published on 25 Apr 2020 - 17:14

score 56 · Answer 11 · 2020-04-26 04:55:08

56

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Prove that if $4k+1$ is a prime number than for every $n \in \mathbb{N}$ $\sum\limits_{j=1}^{2k}{j^{4n+2}}$ is a multiple of $4k+1$

Published on 26 Apr 2020 - 4:55

score 120 · Answer 12 · 2026-04-09 22:40:39

120

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Proof by induction - Fibonacci

Published on 09 Apr 2026 - 22:40

score 78 · Answer 13 · 2026-03-30 06:08:56

78

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proof $k!j!\leq(j+k)!$ by induction

Published on 30 Mar 2026 - 6:08

score 1.1k · Answer 14 · 2026-03-30 08:18:26

1.1k

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Proof of explicit formula for recursive sequence by induction

Published on 30 Mar 2026 - 8:18

score 37 · Answer 15 · 2020-04-26 20:14:10

37

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Prove by induction that the integral exists

Published on 26 Apr 2020 - 20:14

List Question

Use Mathematical Induction to prove that for all integers $n\geq 5, 1+4n<2^n$

Prove by induction $u_{n+2}+u_n=4u_{n+1}$ for all $n\in \mathbb{N}$, where $u_n=(2+\sqrt{3})^n+(2-\sqrt{3})^n$.

Sylvester matrix column orthogonality

Proof by induction of number of edges in complete (fully connected) graph

Induction based on the 2-cocycle identity for $c': \Bbb Z/p \times \Bbb Z/p \to \Bbb Z/p$ and $c'(0, 0) = 0$

Proving $\frac{b-a}{b-x}\cdot (\frac{b-a}{k+1})^{k+1}\geq (\frac{b-a}{k})^{k+1}$

Proving $1 + 2 + 2^2+2^3 + 2^4 + \dots+ 2^{n-1}= 2^n -1$ using mathematical induction

Questions about induction and Big O

Prove the following statements about the geometric sum.

beginner with induction, something I don't understand

Prove that if $4k+1$ is a prime number than for every $n \in \mathbb{N}$ $\sum\limits_{j=1}^{2k}{j^{4n+2}}$ is a multiple of $4k+1$

Proof by induction - Fibonacci

proof $k!j!\leq(j+k)!$ by induction

Proof of explicit formula for recursive sequence by induction

Prove by induction that the integral exists

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