Question

Can all integers be written as $\sum_{i=0}^{N}(-1)^{i}n_{i}2^{i}$ ($n_{i}\in\{0,1\}$)?

score 151 · Answer 1 · 2026-03-28 03:55:31

151

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Can all integers be written as $\sum_{i=0}^{N}(-1)^{i}n_{i}2^{i}$ ($n_{i}\in\{0,1\}$)?

Published on 28 Mar 2026 - 3:55

score 190 · Answer 2 · 2019-09-11 21:40:23

190

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Proof of asymptotic relation $\sum_{i=1}^n i^k = \Theta(n^{ k+1} )$

Published on 11 Sep 2019 - 21:40

score 272 · Answer 3 · 2026-03-26 04:30:03

272

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Why Induction Axiom is needed if structural induction holds

Published on 26 Mar 2026 - 4:30

score 56 · Answer 4 · 2026-03-26 22:55:33

Prove that $a_1 ≤ a_3 ≤ \cdots ≤ a_{2n+1} ≤ a_{2n} ≤ a_{2n-2} ≤ \cdots ≤ a_2$ where $a_i=f_{i+1}/f_i$ and $\{f_i\}$ is the Fibonacci sequence

score 210 · Answer 5 · 2026-03-29 15:14:49

210

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Divisibility result by induction: $64 \mid 3^{2n + 2} - 8n - 9$

Published on 29 Mar 2026 - 15:14

score 161 · Answer 6 · 2026-03-28 22:53:29

161

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How can I prove this sequence is decreasing WITHOUT using induction?

Published on 28 Mar 2026 - 22:53

score 401 · Answer 7 · 2019-09-12 13:23:10

401

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Help in a mathematical induction problem involving a chess board.

Published on 12 Sep 2019 - 13:23

score 70 · Answer 8 · 2019-09-12 14:48:48

70

Views

How does Mathematical Induction work?

Published on 12 Sep 2019 - 14:48

score 84 · Answer 9 · 2026-03-26 04:29:11

84

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How to approach solving this induction problem?

Published on 26 Mar 2026 - 4:29

score 197 · Answer 10 · 2026-03-27 00:04:26

197

Views

Is this a valid weak induction proof on the number of branches in a tree? what would be a strong induction version?

Published on 27 Mar 2026 - 0:04

score 316 · Answer 11 · 2026-03-28 22:31:17

316

Views

Proof of convergence of projected gradient descent via induction

Published on 28 Mar 2026 - 22:31

score 58 · Answer 12 · 2019-09-14 05:17:50

58

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How to prove $~a+aq+\cdots+aq^r = \dfrac{a(q^{r+1}-1)}{q-1}~$ via induction?

Published on 14 Sep 2019 - 5:17

score 78 · Answer 13 · 2019-09-14 11:11:39

Induction: when $a_k=a_0+(k-1)d$ for any non-negative integer $k$, prove $\sum_{i=1}^n a_i=\frac{n(a_1+a_n)}{2}$

score 32 · Answer 14 · 2019-09-14 12:48:18

32

Views

How do I go from the first expression to the second?

Published on 14 Sep 2019 - 12:48

score 87 · Answer 15 · 2019-09-14 22:52:37

87

Views

Proving by induction $P_n : (2n-1)! \leq n^{2n-1}$

Published on 14 Sep 2019 - 22:52

List Question

Can all integers be written as $\sum_{i=0}^{N}(-1)^{i}n_{i}2^{i}$ ($n_{i}\in\{0,1\}$)?

Proof of asymptotic relation $\sum_{i=1}^n i^k = \Theta(n^{ k+1} )$

Why Induction Axiom is needed if structural induction holds

Prove that $a_1 ≤ a_3 ≤ \cdots ≤ a_{2n+1} ≤ a_{2n} ≤ a_{2n-2} ≤ \cdots ≤ a_2$ where $a_i=f_{i+1}/f_i$ and $\{f_i\}$ is the Fibonacci sequence

Divisibility result by induction: $64 \mid 3^{2n + 2} - 8n - 9$

How can I prove this sequence is decreasing WITHOUT using induction?

Help in a mathematical induction problem involving a chess board.

How does Mathematical Induction work?

How to approach solving this induction problem?

Is this a valid weak induction proof on the number of branches in a tree? what would be a strong induction version?

Proof of convergence of projected gradient descent via induction

How to prove $~a+aq+\cdots+aq^r = \dfrac{a(q^{r+1}-1)}{q-1}~$ via induction?

Induction: when $a_k=a_0+(k-1)d$ for any non-negative integer $k$, prove $\sum_{i=1}^n a_i=\frac{n(a_1+a_n)}{2}$

How do I go from the first expression to the second?

Proving by induction $P_n : (2n-1)! \leq n^{2n-1}$

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