Слайд 2
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-1.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 3
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-2.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 4
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-3.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 5
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-4.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 6
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-5.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 7
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-6.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 8
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-7.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 9
![Linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-8.jpg)
Linear homogeneous recurrence relations
with constant coefficients
Слайд 10
![Solving linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-9.jpg)
Solving linear homogeneous recurrence relations
with constant coefficients
Слайд 11
![Solving linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-10.jpg)
Solving linear homogeneous recurrence relations
with constant coefficients
Слайд 12
![Solving linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-11.jpg)
Solving linear homogeneous recurrence relations
with constant coefficients
Слайд 13
![Solving linear homogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-12.jpg)
Solving linear homogeneous recurrence relations
with constant coefficients
Слайд 14
![Solving linear homogeneous recurrence relations with constant coefficients As we](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-13.jpg)
Solving linear homogeneous recurrence relations
with constant coefficients
As we will see, these
characteristic roots can be used to give an explicit formula for all the solutions of the recurrence relation.
Слайд 15
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-14.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 16
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-15.jpg)
Слайд 17
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-16.jpg)
Слайд 18
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-17.jpg)
Слайд 19
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-18.jpg)
Слайд 20
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-19.jpg)
Слайд 21
![Proof of theorem 1](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-20.jpg)
Слайд 22
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-21.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 23
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-22.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 24
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-23.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 25
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-24.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 26
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-25.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 27
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-26.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 28
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-27.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 29
![Solving linear homogeneous recurrence relations with constant coefficients of degree two](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-28.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree two
Слайд 30
![Solving linear homogeneous recurrence relations with constant coefficients of degree three](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-29.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree three
Слайд 31
![Solving linear homogeneous recurrence relations with constant coefficients of degree three](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-30.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree three
Слайд 32
![Solving linear homogeneous recurrence relations with constant coefficients of degree three](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-31.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree three
Слайд 33
![Solving linear homogeneous recurrence relations with constant coefficients of degree three](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-32.jpg)
Solving linear homogeneous recurrence relations with constant coefficients of degree three
Слайд 34
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-33.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 35
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-34.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 36
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-35.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 37
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-36.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 38
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-37.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 39
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-38.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 40
![Proof of theorem 4](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-39.jpg)
Слайд 41
![Proof of theorem 4](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-40.jpg)
Слайд 42
![Proof of theorem 4](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-41.jpg)
Слайд 43
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-42.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 44
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-43.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 45
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-44.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 46
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-45.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients
Слайд 47
![Linear nonhomogeneous recurrence relations with constant coefficients](/_ipx/f_webp&q_80&fit_contain&s_1440x1080/imagesDir/jpg/139538/slide-46.jpg)
Linear nonhomogeneous recurrence relations
with constant coefficients