How can one prove that a characteristic equation can be used to solve homogenous linear recurrence relations??

Asked Dec 01 '23 at 16:44

Active Dec 03 '23 at 14:55

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I have already proved that for degree 2 homogenous linear recurrence relation of degree 2 that it's nth term can be expressed as A^n.C + B^n.D where C an D are constants which can be evaluated using given conditions and A and B are the roots of the characteristic equation.

How can I prove this for degree 3 and also for any k degree? Please give a detailed step-by-step solution because I could not extend my proof from degree 2 to degree 3.

edited Dec 03 '23 at 14:55

asked Dec 01 '23 at 16:44

Adhvik

The same proof should work. Note, though, that you need to take care when there are roots with multiplicity. – lulu Dec 01 '23 at 17:08

How can one prove that a characteristic equation can be used to solve homogenous linear recurrence relations??

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