Question

If $x_1 = 3$, $x_{n+1} = \frac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is bounded below by $0$, above by $4$.

score 1.5k · Answer 1 · 2026-04-19 13:04:59

1.5k

Views

If $x_1 = 3$, $x_{n+1} = \frac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is bounded below by $0$, above by $4$.

Published on 19 Apr 2026 - 13:04

score 153 · Answer 2 · 2026-04-14 13:43:08

153

Views

Prove the all cheaters will be killed

Published on 14 Apr 2026 - 13:43

score 61 · Answer 3 · 2026-04-10 13:25:02

61

Views

proof by induction (summations)

Published on 10 Apr 2026 - 13:25

score 538 · Answer 4 · 2026-04-14 10:45:40

538

Views

proof by induction (derivative of $x^n=n!$)

Published on 14 Apr 2026 - 10:45

score 155 · Answer 5 · 2026-04-16 01:19:18

155

Views

Induction proof of $\ln(1+1/n) \leq 1/n$ fails even though it is true

Published on 16 Apr 2026 - 1:19

score 298 · Answer 6 · 2026-04-09 04:23:28

298

Views

Can the Principle of Mathematical induction be generalized?

Published on 09 Apr 2026 - 4:23

score 84 · Answer 7 · 2026-04-14 20:14:00

84

Views

Prove by induction that the sum of the terms in a sequence is: $\frac{a_0 - a_{n+1} }{1 - r} $

Published on 14 Apr 2026 - 20:14

score 128 · Answer 8 · 2026-04-15 07:49:52

128

Views

Prove that for all $n\ge9$, there exist natural numbers $x,y$ such that $n=2x+5y$.

Published on 15 Apr 2026 - 7:49

score 77 · Answer 9 · 2026-04-16 01:21:14

77

Views

Prove that for all x $\in \mathbb{N}$ it holds that the number a(n) := $x^2$ + 4x + 3 has a non-trivial divisor

Published on 16 Apr 2026 - 1:21

score 178 · Answer 10 · 2026-04-11 06:02:03

178

Views

Proof by Induction involving divisibility

Published on 11 Apr 2026 - 6:02

score 167 · Answer 11 · 2026-04-13 17:29:42

167

Views

Proving sets are infinite.

Published on 13 Apr 2026 - 17:29

score 173 · Answer 12 · 2026-04-09 15:26:06

173

Views

Show that $A_n$ for $n>4$ is generated by the stabilizers from $1$ to $n$.

Published on 09 Apr 2026 - 15:26

score 127 · Answer 13 · 2026-04-15 23:28:17

127

Views

Induction proof: $\sqrt{\sum_{i=1}^na_i^2}\leq\sum_{i=1}^n\sqrt{a_i^2}$

Published on 15 Apr 2026 - 23:28

score 121 · Answer 14 · 2026-04-18 16:20:37

121

Views

induction regarding the binomial coefficient

Published on 18 Apr 2026 - 16:20

score 90 · Answer 15 · 2026-04-12 16:49:12

90

Views

Infinite subset of infinite subset of $\mathbb{N}$

Published on 12 Apr 2026 - 16:49

List Question

If $x_1 = 3$, $x_{n+1} = \frac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is bounded below by $0$, above by $4$.

Prove the all cheaters will be killed

proof by induction (summations)

proof by induction (derivative of $x^n=n!$)

Induction proof of $\ln(1+1/n) \leq 1/n$ fails even though it is true

Can the Principle of Mathematical induction be generalized?

Prove by induction that the sum of the terms in a sequence is: $\frac{a_0 - a_{n+1} }{1 - r} $

Prove that for all $n\ge9$, there exist natural numbers $x,y$ such that $n=2x+5y$.

Prove that for all x $\in \mathbb{N}$ it holds that the number a(n) := $x^2$ + 4x + 3 has a non-trivial divisor

Proof by Induction involving divisibility

Proving sets are infinite.

Show that $A_n$ for $n>4$ is generated by the stabilizers from $1$ to $n$.

Induction proof: $\sqrt{\sum_{i=1}^na_i^2}\leq\sum_{i=1}^n\sqrt{a_i^2}$

induction regarding the binomial coefficient

Infinite subset of infinite subset of $\mathbb{N}$

Trending Questions

Popular # Hahtags

Popular Questions