[Discrete Mathematics] Nonhomogeneous Recurrence Relation Examples

We solve a couple simple nonhomogeneous recurrence relations.

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[azra]

you are such a legend I've watched your recurrence videos and I have my exam in 1 day and I finally got it how to do recursion after struggeling and feeling stupid whole semester
such.a.fucking.good.teacher.

[LemesaElias]

I think I'm gonna pass all of my discrete mathematics exams with your videos in my pockets.

[aqsayounus]

But what if I wanna do the first question with characteristic roots method. How will we deal with f(n) = n?

[yenzyhebron]

I tried answering your first example by solving for the homogenous and particular solution separately but I didn't get the right answer. If we have the form a_n - a_(n-1) = f(n) is our option really just to use the a_n = a_0 + summation f(i) range(i=1, n)?
Edit: I got it now, but I used (An+B)n as a trial particular solution instead of An+B, but why does (An+B)n work but not An+B?

[SamSarwat]

please I'm going mad here. When I use the guessing method, that is a^p= cn^2 + dn, i get a different solutions and it doesn't make sense WHy

[shibaditya]

u say that if A(n)=A(n-1)+f(n) then solve that this way but if the question A(n)=A(n-1)+A(n-2)+f(n) then how can we solve this?

[shubhamgoswami]

If a nth term + a n+1 th term = f(n) ...will this formula works ???

[Chandler]

I believe you need induction proof to derive the sigma function

[mohammedadem]

Thanks for sharing your know trev, i was really helpful!

[ilhamrizkianto]

Could you please explain why this method doesn't work for a_n = a_(n-1)+1, a_n=0 ? Thanks

[murdamurda]

what do we do if there's a constant at a sub n-1 or a sub n?

[MandeepKaur-giwl]

If ao is not given in the question then???

[abeerqamer]

Has anyone solved these examples by using the method used in the previous video?

[mohammedadem]

please give me solution of an=2an-1+2n2; a1=4

[garuda_]

Please do solve this one
an+2 - 6an+1 +9an = 3(2 to the power n) + 7 (3 to the power n ), n>=0 ; a0 = 1 and a1 =4

[alienpuppy]

Thanks for sharing your know trev, i was really helpful!