Question

Prove using induction that $(2^n)+1<3^n$ for all natural numbers, $n>=2$

score 70 · Answer 1 · 2018-11-08 02:23:12

70

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Prove using induction that $(2^n)+1<3^n$ for all natural numbers, $n>=2$

Published on 08 Nov 2018 - 2:23

score 30 · Answer 2 · 2018-11-08 10:19:40

30

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Proving the existence of $f:\mathbb{Z}_2^{n} \rightarrow n$ under some conditions... iff $n=2^m$

Published on 08 Nov 2018 - 10:19

score 157 · Answer 3 · 2018-11-08 23:52:52

157

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Proof by induction with unknown formula?

Published on 08 Nov 2018 - 23:52

score 86 · Answer 4 · 2026-03-26 02:56:22

86

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For $s, t \in \{-\lfloor (n-1)/2 \rfloor, \dots, -1, 0, 1, \dots, \lfloor n/2 \rfloor \}$, $n \in \mathbb{Z}_{ > 0}$, show $s-t \neq \ell n$

Published on 26 Mar 2026 - 2:56

score 82 · Answer 5 · 2026-03-27 14:21:23

82

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Logical Induction

Published on 27 Mar 2026 - 14:21

score 641 · Answer 6 · 2026-03-27 06:51:59

641

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Prove that $x² + y² = z^n$ has a solution in $\mathbb{N}$, for all $n$ belonging to the set of natural numbers

Published on 27 Mar 2026 - 6:51

score 54 · Answer 7 · 2018-11-09 22:58:50

54

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Prove that $n/2 < 1/1 + 1/2 +1/3 + 1/4 +1/5 + 1/6 + ... + 1/2^{n-1} \le n$. n is a natural ,$n \ge 1$. Induction.

Published on 09 Nov 2018 - 22:58

score 93 · Answer 8 · 2018-11-10 05:36:04

93

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How to show $\frac{1}{2}+\frac{2}{4}+\frac{3}{8}+...+\frac{n}{2^n}<2$ using induction

Published on 10 Nov 2018 - 5:36

score 321 · Answer 9 · 2018-11-10 17:48:07

321

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Verifying the validity of a structural induction proof

Published on 10 Nov 2018 - 17:48

score 2.2k · Answer 10 · 2026-03-26 06:12:42

2.2k

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Prove the Fibonacci Sequence by induction (Sigma F2i+1)=F2n

Published on 26 Mar 2026 - 6:12

score 85 · Answer 11 · 2018-11-11 05:43:15

85

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Mathematical Induction: For all n∈N and p∈R with p>=-1; 1+np<=(1+p)^n

Published on 11 Nov 2018 - 5:43

score 104 · Answer 12 · 2026-03-26 11:17:31

104

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Proving that first-order formulas can not distinguish sets of a certain size

Published on 26 Mar 2026 - 11:17

score 199 · Answer 13 · 2018-11-11 13:47:59

199

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How to prove this mathematical induction?

Published on 11 Nov 2018 - 13:47

score 1.9k · Answer 14 · 2018-11-11 19:18:01

1.9k

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Prove that if there are no cycles of length 3, there must be at least 2n vertices.

Published on 11 Nov 2018 - 19:18

score 112 · Answer 15 · 2018-11-12 03:12:57

112

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Some questions about proving with induction

Published on 12 Nov 2018 - 3:12

List Question

Prove using induction that $(2^n)+1<3^n$ for all natural numbers, $n>=2$

Proving the existence of $f:\mathbb{Z}_2^{n} \rightarrow n$ under some conditions... iff $n=2^m$

Proof by induction with unknown formula?

For $s, t \in \{-\lfloor (n-1)/2 \rfloor, \dots, -1, 0, 1, \dots, \lfloor n/2 \rfloor \}$, $n \in \mathbb{Z}_{ > 0}$, show $s-t \neq \ell n$

Logical Induction

Prove that $x² + y² = z^n$ has a solution in $\mathbb{N}$, for all $n$ belonging to the set of natural numbers

Prove that $n/2 < 1/1 + 1/2 +1/3 + 1/4 +1/5 + 1/6 + ... + 1/2^{n-1} \le n$. n is a natural ,$n \ge 1$. Induction.

How to show $\frac{1}{2}+\frac{2}{4}+\frac{3}{8}+...+\frac{n}{2^n}<2$ using induction

Verifying the validity of a structural induction proof

Prove the Fibonacci Sequence by induction (Sigma F2i+1)=F2n

Mathematical Induction: For all n∈N and p∈R with p>=-1; 1+np<=(1+p)^n

Proving that first-order formulas can not distinguish sets of a certain size

How to prove this mathematical induction?

Prove that if there are no cycles of length 3, there must be at least 2n vertices.

Some questions about proving with induction

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