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Proving $n \lt 2^n$ for $n\geq 1$ using induction

score 166 · Answer 1 · 2026-04-16 23:23:39

166

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Proving $n \lt 2^n$ for $n\geq 1$ using induction

Published on 16 Apr 2026 - 23:23

score 9.5k · Answer 2 · 2026-04-13 03:25:37

9.5k

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Is there a general rule for how to pick the base case value for proofs by mathematical induction?

Published on 13 Apr 2026 - 3:25

score 73 · Answer 3 · 2026-04-10 01:58:14

73

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How do I write $2(2^k+1) - 1$ as $(2 \cdot 2^k + 1)$?

Published on 10 Apr 2026 - 1:58

score 427 · Answer 4 · 2026-04-16 14:09:17

427

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How to find variance of k+1 elements if variance of k elements is known?

Published on 16 Apr 2026 - 14:09

score 200 · Answer 5 · 2026-04-17 00:29:03

200

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Prove by induction that $4$ divides $n^3+(n+1)^3+(n+2)^3+(n+3)^3$

Published on 17 Apr 2026 - 0:29

score 1.3k · Answer 6 · 2026-04-09 07:09:02

1.3k

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general formula using informal inductive reasoning

Published on 09 Apr 2026 - 7:09

score 385 · Answer 7 · 2026-04-15 03:36:25

385

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Using induction to prova a regular expression belongs to the language generated by a grammar (well half-proving anyways)

Published on 15 Apr 2026 - 3:36

score 2.1k · Answer 8 · 2026-03-25 08:10:04

2.1k

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Proof of Leibniz formula from Laplace expansion

Published on 25 Mar 2026 - 8:10

score 71 · Answer 9 · 2026-04-16 12:10:24

INDUCTION: Let a sequence of numbers $a_n$ for $n\in \mathbb N$ be defined by the following rule: $a_1 = 1$, and for $n>1$, $a_n = 2a_{n-1} + 1$

score 178 · Answer 10 · 2026-04-16 01:19:11

178

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Induction, 0'1 and 1's sequence fun question

Published on 16 Apr 2026 - 1:19

score 1.6k · Answer 11 · 2026-04-11 05:28:26

1.6k

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Finding the error in this induction proof

Published on 11 Apr 2026 - 5:28

score 385 · Answer 12 · 2026-04-09 21:37:36

385

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Proof of Natural set to any power k, is countably infinite

Published on 09 Apr 2026 - 21:37

score 2k · Answer 13 · 2026-04-12 00:38:32

2k

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Proof by induction that $3^{2n} + 7$ is divisible by $4$

Published on 12 Apr 2026 - 0:38

score 2k · Answer 14 · 2026-05-05 01:15:56

2k

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Strong Induction to prove $T(n)$ is $O(n)$ for $T(n) = T(\lfloor n/3 \rfloor) + T(\lfloor n/5 \rfloor) + T(\lfloor n/7 \rfloor) + n$

Published on 05 May 2026 - 1:15

score 173 · Answer 15 · 2026-04-16 07:24:07

173

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proof by induction $2^n \leq 2^{n+1}-2^{n−1}-1$

Published on 16 Apr 2026 - 7:24

List Question

Proving $n \lt 2^n$ for $n\geq 1$ using induction

Is there a general rule for how to pick the base case value for proofs by mathematical induction?

How do I write $2(2^k+1) - 1$ as $(2 \cdot 2^k + 1)$?

How to find variance of k+1 elements if variance of k elements is known?

Prove by induction that $4$ divides $n^3+(n+1)^3+(n+2)^3+(n+3)^3$

general formula using informal inductive reasoning

Using induction to prova a regular expression belongs to the language generated by a grammar (well half-proving anyways)

Proof of Leibniz formula from Laplace expansion

INDUCTION: Let a sequence of numbers $a_n$ for $n\in \mathbb N$ be defined by the following rule: $a_1 = 1$, and for $n>1$, $a_n = 2a_{n-1} + 1$

Induction, 0'1 and 1's sequence fun question

Finding the error in this induction proof

Proof of Natural set to any power k, is countably infinite

Proof by induction that $3^{2n} + 7$ is divisible by $4$

Strong Induction to prove $T(n)$ is $O(n)$ for $T(n) = T(\lfloor n/3 \rfloor) + T(\lfloor n/5 \rfloor) + T(\lfloor n/7 \rfloor) + n$

proof by induction $2^n \leq 2^{n+1}-2^{n−1}-1$

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