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Struggling with a strong induction problem involving recurrence relations

score 3.6k · Answer 1 · 2026-04-10 21:55:03

3.6k

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Struggling with a strong induction problem involving recurrence relations

Published on 10 Apr 2026 - 21:55

score 76 · Answer 2 · 2026-04-10 18:41:45

76

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How can I deal with recurrent sequences?

Published on 10 Apr 2026 - 18:41

score 196 · Answer 3 · 2026-03-29 20:51:48

196

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Show that ${(F_n^2+F_{n+1}^2+F_{n+2}^2)^2\over F_{n}^4+F_{n+1}^4+F_{n+2}^4}=2$

Published on 29 Mar 2026 - 20:51

score 960 · Answer 4 · 2026-04-13 06:58:26

960

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Solve the recurrence and verify the formula using strong induction

Published on 13 Apr 2026 - 6:58

score 27 · Answer 5 · 2026-04-01 12:47:17

27

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Time Complexity for a recurrence

Published on 01 Apr 2026 - 12:47

score 4.8k · Answer 6 · 2026-04-11 17:08:16

4.8k

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Solving two-dimensional recurrence relation $a_{i,\ j}\ =\ a_{i,\ j-1}\ +\ a_{i-1,\ j-1}$

Published on 11 Apr 2026 - 17:08

score 53 · Answer 7 · 2016-12-20 04:33:52

53

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General form of $a_n$ given $ a_n=2a_{n-1}+2^{n-1} $, $a_2=4$, $a_3=12$

Published on 20 Dec 2016 - 4:33

score 155 · Answer 8 · 2026-03-29 20:51:50

155

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Show that $S_L= L_n^2L_{n+1} -L_1L_2L_3-L_2L_3L_4-\cdots L_{n-2}L_{n-1}L_n$, $n\ge3$

Published on 29 Mar 2026 - 20:51

score 187 · Answer 9 · 2026-03-29 20:51:50

187

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How can we show that $2^3+1^3+3^3+4^3+\cdots+L_n^3={L_nL_{n+1}^2+5(-1)^n[L_{n-1}+2(-1)^n]+9\over 2}$

Published on 29 Mar 2026 - 20:51

score 135 · Answer 10 · 2026-04-12 02:17:41

135

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Homogenous Recurrence with Quadratic Coefficients

Published on 12 Apr 2026 - 2:17

score 516 · Answer 11 · 2016-12-24 17:30:05

516

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Proof by induction for recursive sequence $a_n =a_{\lfloor n/2 \rfloor} + a_{\lceil n/2 \rceil} +3n +1$

Published on 24 Dec 2016 - 17:30

score 114 · Answer 12 · 2016-12-24 23:02:08

114

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How to solve this recurrence relation? $a_n=(a_{n-1})^3\cdot a_{n-2}$

Published on 24 Dec 2016 - 23:02

score 76 · Answer 13 · 2026-04-09 14:56:13

76

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How to solve the following recurrence equation?

Published on 09 Apr 2026 - 14:56

score 37 · Answer 14 · 2026-04-13 08:24:04

37

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Functions That Also Satisfy Binomial Distribution Recurrence

Published on 13 Apr 2026 - 8:24

score 900 · Answer 15 · 2026-04-12 08:53:57

900

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Finding the limit of a contractive sequence

Published on 12 Apr 2026 - 8:53

List Question

Struggling with a strong induction problem involving recurrence relations

How can I deal with recurrent sequences?

Show that ${(F_n^2+F_{n+1}^2+F_{n+2}^2)^2\over F_{n}^4+F_{n+1}^4+F_{n+2}^4}=2$

Solve the recurrence and verify the formula using strong induction

Time Complexity for a recurrence

Solving two-dimensional recurrence relation $a_{i,\ j}\ =\ a_{i,\ j-1}\ +\ a_{i-1,\ j-1}$

General form of $a_n$ given $ a_n=2a_{n-1}+2^{n-1} $, $a_2=4$, $a_3=12$

Show that $S_L= L_n^2L_{n+1} -L_1L_2L_3-L_2L_3L_4-\cdots L_{n-2}L_{n-1}L_n$, $n\ge3$

How can we show that $2^3+1^3+3^3+4^3+\cdots+L_n^3={L_nL_{n+1}^2+5(-1)^n[L_{n-1}+2(-1)^n]+9\over 2}$

Homogenous Recurrence with Quadratic Coefficients

Proof by induction for recursive sequence $a_n =a_{\lfloor n/2 \rfloor} + a_{\lceil n/2 \rceil} +3n +1$

How to solve this recurrence relation? $a_n=(a_{n-1})^3\cdot a_{n-2}$

How to solve the following recurrence equation?

Functions That Also Satisfy Binomial Distribution Recurrence

Finding the limit of a contractive sequence

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