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Homework Statement
Here's my problem - Give the order of linear homogeneous recurrence relations with constant coefficients for: An = 2na(n-1)
=2(2An-1 + 1) + 1
=2^2An-1 + 2 + 1
A linear homogeneous recurrence relation is a mathematical equation that describes the relationship between a sequence of numbers, where each term is a constant multiple of the previous term. It can be represented in the form of a recurrence relation, where each term is expressed in terms of the previous term(s).
There are several methods for solving a linear homogeneous recurrence relation, including the characteristic equation method, the substitution method, and the generating function method. The method you use will depend on the specific form of the recurrence relation and your own personal preference.
The characteristic equation method is a technique for solving linear homogeneous recurrence relations. It involves finding the roots of the characteristic equation, which is derived from the recurrence relation. The solutions to the characteristic equation are then used to find the general solution to the recurrence relation.
The substitution method is a technique for solving linear homogeneous recurrence relations. It involves substituting a proposed solution into the recurrence relation and solving for the unknown coefficients. This method is useful when the recurrence relation is in a specific form, such as a Fibonacci sequence.
The generating function method is a technique for solving linear homogeneous recurrence relations. It involves representing the sequence of numbers as a power series, and then manipulating the series to find a closed form formula for the terms. This method is useful for solving more complex recurrence relations.