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Find the roots of $\lambda^8 -2\lambda^7+1=0$ (characteristic polynomial)

score 106 · Answer 1 · 2026-04-16 06:12:36

106

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Find the roots of $\lambda^8 -2\lambda^7+1=0$ (characteristic polynomial)

Published on 16 Apr 2026 - 6:12

score 58 · Answer 2 · 2026-04-16 20:04:53

58

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$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Published on 16 Apr 2026 - 20:04

score 103 · Answer 3 · 2026-04-16 15:30:42

103

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Write $b_{n+1}$ in terms of $b_n$, where $b_n=\frac{2a_0a_1a_2...a_{n-1}}{a_n}\forall n\ge1$

Published on 16 Apr 2026 - 15:30

score 47 · Answer 4 · 2026-04-16 11:41:55

47

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Solution of recurrence relation $T(n) = \sum_{i=0}^{n-1}T(i) + n$

Published on 16 Apr 2026 - 11:41

score 37 · Answer 5 · 2026-04-12 17:36:01

37

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Prob. 20, Sec. 2.2, in Leon's Linear Algebra Book: Numbers of additions and multiplications in calculation of the determinant

Published on 12 Apr 2026 - 17:36

score 230 · Answer 6 · 2026-04-15 21:08:59

230

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Find the number of collections of $16$ distinct subsets of $\{1,2,3,4,5\}$ with the some specific property

Published on 15 Apr 2026 - 21:08

score 142 · Answer 7 · 2026-04-10 02:03:18

142

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Recurrence Relation for Bayes' Theorem

Published on 10 Apr 2026 - 2:03

score 70 · Answer 8 · 2026-04-17 05:31:16

70

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Recursion for counting valid strings (Generatingfunctionology chapter 1, problem 20)

Published on 17 Apr 2026 - 5:31

score 152 · Answer 9 · 2026-04-10 21:49:04

152

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Basic Functional Equation

Published on 10 Apr 2026 - 21:49

score 64 · Answer 10 · 2026-04-17 07:02:48

64

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A question on binary system.

Published on 17 Apr 2026 - 7:02

score 79 · Answer 11 · 2026-04-15 20:07:06

79

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$a_1>0$ and $a_{n+1}=\ln{(a_n+1)}$. Where is the largest term of the sequence $na_n$?

Published on 15 Apr 2026 - 20:07

score 66 · Answer 12 · 2026-04-14 06:07:29

Showing that a given recurrence relationship equals sin(nx) - please advise me how to come to a conclusion at the end?

score 151 · Answer 13 · 2026-04-15 12:54:34

151

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How to know some equation can be solved or not arithmetically?

Published on 15 Apr 2026 - 12:54

score 80 · Answer 14 · 2026-04-14 00:48:43

80

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Hard limit of a sequence defined by recurrence

Published on 14 Apr 2026 - 0:48

score 33 · Answer 15 · 2026-04-11 12:59:30

33

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Establishing Recurrence Relation for Legendre Polynomials using Rodrigues' Formula

Published on 11 Apr 2026 - 12:59

List Question

Find the roots of $\lambda^8 -2\lambda^7+1=0$ (characteristic polynomial)

$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Write $b_{n+1}$ in terms of $b_n$, where $b_n=\frac{2a_0a_1a_2...a_{n-1}}{a_n}\forall n\ge1$

Solution of recurrence relation $T(n) = \sum_{i=0}^{n-1}T(i) + n$

Prob. 20, Sec. 2.2, in Leon's Linear Algebra Book: Numbers of additions and multiplications in calculation of the determinant

Find the number of collections of $16$ distinct subsets of $\{1,2,3,4,5\}$ with the some specific property

Recurrence Relation for Bayes' Theorem

Recursion for counting valid strings (Generatingfunctionology chapter 1, problem 20)

Basic Functional Equation

A question on binary system.

$a_1>0$ and $a_{n+1}=\ln{(a_n+1)}$. Where is the largest term of the sequence $na_n$?

Showing that a given recurrence relationship equals sin(nx) - please advise me how to come to a conclusion at the end?

How to know some equation can be solved or not arithmetically?

Hard limit of a sequence defined by recurrence

Establishing Recurrence Relation for Legendre Polynomials using Rodrigues' Formula

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