Question

Proving the series $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$ is not bounded

score 85 · Answer 1 · 2020-05-17 14:38:44

85

Views

Proving the series $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$ is not bounded

Published on 17 May 2020 - 14:38

score 58 · Answer 2 · 2026-04-11 19:08:13

58

Views

Proof of divisibility by induction

Published on 11 Apr 2026 - 19:08

score 85 · Answer 3 · 2020-05-18 03:44:39

85

Views

Prove an algorithm on the Thue-Morse sequence by induction

Published on 18 May 2020 - 3:44

score 92 · Answer 4 · 2020-05-19 17:17:37

92

Views

In one-step induction, why sometimes there are 2 base cases?

Published on 19 May 2020 - 17:17

score 55 · Answer 5 · 2020-05-20 14:51:13

55

Views

Proving finite amount of 'non-cool' numbers

Published on 20 May 2020 - 14:51

score 523 · Answer 6 · 2020-05-20 16:24:05

523

Views

Proving by induction that $(5^{2n})-1$ is divisible by $8$ and $3$

Published on 20 May 2020 - 16:24

score 434 · Answer 7 · 2026-04-08 22:40:20

434

Views

Show if $x_1=1, x_2=2, x_n=\frac{1}{2}(x_{n-1}+x_{n-2})$, then $1\le x_n \le 2$ for all $n\in\mathbb{N}$ using Strong Induction

Published on 08 Apr 2026 - 22:40

score 66 · Answer 8 · 2020-05-20 20:00:21

66

Views

Prove that $\sum_{i=0}^{n-1} {2^i} = 2^n -1$

Published on 20 May 2020 - 20:00

score 29 · Answer 9 · 2026-03-27 01:13:25

29

Views

Convergence of two nested geometric sequences

Published on 27 Mar 2026 - 1:13

score 119 · Answer 10 · 2020-05-21 04:21:10

119

Views

Recursive sequence, $x_{1} \geq 0, x_{n+1}=\sqrt{x_{n}+2}$

Published on 21 May 2020 - 4:21

score 130 · Answer 11 · 2020-05-21 13:37:18

130

Views

Prove by induction that for all $n\in\mathbb N, (\sqrt3+i)^n+(\sqrt3-i)^n=2^{n+1}\cos(\frac{n\pi}6)$

Published on 21 May 2020 - 13:37

score 234 · Answer 12 · 2026-04-09 10:06:31

234

Views

Floyd Invariant Principle on a deck of cards

Published on 09 Apr 2026 - 10:06

score 42 · Answer 13 · 2026-04-09 19:10:24

42

Views

Mathematical induction method for a problem

Published on 09 Apr 2026 - 19:10

score 690 · Answer 14 · 2026-04-11 04:45:06

690

Views

Math Induction proof union and intersections

Published on 11 Apr 2026 - 4:45

score 77 · Answer 15 · 2026-03-30 05:26:27

77

Views

Proof verification: Showing, through Induction, that a set $S=\mathbb{N}$

Published on 30 Mar 2026 - 5:26

List Question

Proving the series $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$ is not bounded

Proof of divisibility by induction

Prove an algorithm on the Thue-Morse sequence by induction

In one-step induction, why sometimes there are 2 base cases?

Proving finite amount of 'non-cool' numbers

Proving by induction that $(5^{2n})-1$ is divisible by $8$ and $3$

Show if $x_1=1, x_2=2, x_n=\frac{1}{2}(x_{n-1}+x_{n-2})$, then $1\le x_n \le 2$ for all $n\in\mathbb{N}$ using Strong Induction

Prove that $\sum_{i=0}^{n-1} {2^i} = 2^n -1$

Convergence of two nested geometric sequences

Recursive sequence, $x_{1} \geq 0, x_{n+1}=\sqrt{x_{n}+2}$

Prove by induction that for all $n\in\mathbb N, (\sqrt3+i)^n+(\sqrt3-i)^n=2^{n+1}\cos(\frac{n\pi}6)$

Floyd Invariant Principle on a deck of cards

Mathematical induction method for a problem

Math Induction proof union and intersections

Proof verification: Showing, through Induction, that a set $S=\mathbb{N}$

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