Question

Sequence $< x_n >$ be defined by $x_1=1; x_2=2;$ and for $n \geq 3$ by $x_n =(x_{n-1} + x_{n-2}) / 2$. Prove $1 \leq x_n \leq 3$

score 266 · Answer 1 · 2026-04-17 05:33:19

Sequence $< x_n >$ be defined by $x_1=1; x_2=2;$ and for $n \geq 3$ by $x_n =(x_{n-1} + x_{n-2}) / 2$. Prove $1 \leq x_n \leq 3$

score 1.2k · Answer 2 · 2026-04-14 16:09:08

1.2k

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Induction: Prove that any integer postage greater than 34 cents can be formed using only 5-cent and 9-cent stamps

Published on 14 Apr 2026 - 16:09

score 69 · Answer 3 · 2026-04-12 23:22:59

69

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How to prove this statement about the Fibonacci Sequence using induction?

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score 54 · Answer 4 · 2026-04-11 02:28:45

54

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How to prove this statement through induction?

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score 162 · Answer 5 · 2026-04-12 20:48:11

162

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Mathematical Induction for Recurrence Relation

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score 203 · Answer 6 · 2026-04-12 11:47:44

203

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score 24 · Answer 7 · 2026-04-09 20:19:19

24

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How would you show sequence terms are bound?

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score 101 · Answer 8 · 2026-04-17 11:33:31

101

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Inductive Proofs--Fibonacci Sequence: $F_{2n-1} + F_{2n+1} = F^2_{2n}+1$

Published on 17 Apr 2026 - 11:33

score 102 · Answer 9 · 2026-03-26 01:11:56

102

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lucas numbers Prove that $l_0^2+l_1^2+...+l_n^2=l_n*l_n+1+2$ for $n \ge 0$

Published on 26 Mar 2026 - 1:11

score 181 · Answer 10 · 2026-04-14 10:09:50

181

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Recursive induction proof

Published on 14 Apr 2026 - 10:09

score 124 · Answer 11 · 2026-04-09 22:51:16

124

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Reformulate the strong induction principle as a method for proving that subsets of $\mathbb{Z}^+$ are the whole set.

Published on 09 Apr 2026 - 22:51

score 211 · Answer 12 · 2026-04-16 00:27:00

211

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Proof that $\prod_{k=1}^{n-1}(1+\frac1k)^k = \frac{n^n}{n!}$ for all $n \in \Bbb N \ge 2$

Published on 16 Apr 2026 - 0:27

score 63 · Answer 13 · 2026-04-11 04:19:14

63

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Induction proof of inequality

Published on 11 Apr 2026 - 4:19

score 37 · Answer 14 · 2026-04-15 21:00:17

How to prove via induction that this sequence $a_1=0, a_{2m}= \frac{a_{2m-1}}{2}, a_{2m+1}=\frac{1}{2}+s_{2m}$ has the following form?

score 5.7k · Answer 15 · 2026-04-14 12:11:31

5.7k

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Understanding this proof by strong induction that each n≥12 is n = 3a + 7b for some natural numbers (a,b)

Published on 14 Apr 2026 - 12:11

List Question

Sequence $< x_n >$ be defined by $x_1=1; x_2=2;$ and for $n \geq 3$ by $x_n =(x_{n-1} + x_{n-2}) / 2$. Prove $1 \leq x_n \leq 3$

Induction: Prove that any integer postage greater than 34 cents can be formed using only 5-cent and 9-cent stamps

How to prove this statement about the Fibonacci Sequence using induction?

How to prove this statement through induction?

Mathematical Induction for Recurrence Relation

Prove using Induction | Tricky one!

How would you show sequence terms are bound?

Inductive Proofs--Fibonacci Sequence: $F_{2n-1} + F_{2n+1} = F^2_{2n}+1$

lucas numbers Prove that $l_0^2+l_1^2+...+l_n^2=l_n*l_n+1+2$ for $n \ge 0$

Recursive induction proof

Reformulate the strong induction principle as a method for proving that subsets of $\mathbb{Z}^+$ are the whole set.

Proof that $\prod_{k=1}^{n-1}(1+\frac1k)^k = \frac{n^n}{n!}$ for all $n \in \Bbb N \ge 2$

Induction proof of inequality

How to prove via induction that this sequence $a_1=0, a_{2m}= \frac{a_{2m-1}}{2}, a_{2m+1}=\frac{1}{2}+s_{2m}$ has the following form?

Understanding this proof by strong induction that each n≥12 is n = 3a + 7b for some natural numbers (a,b)

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