Math Is Fun Forum

Nguyen

Guest

solving recurrence relations (checking ans)

Hey people, can anyone tell me if my working is correct for the following 2 recurrence relations I think I solved. I am not too confident with these types of questions

1.

with

particular solution of the form:

particular solution:

general solution of

is:

2.

with

and

solve characteristic equation:

If there are any errors please point them out to me. As I said, I am not too confident with these types of questions.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solving recurrence relations (checking ans)

Hi  Nguyen;

1) Is correct.

2) Is not correct. Your answer does not match the sequence the recurrence would generate.
Always check to see if the 2 match or prove your answer by induction. Here checking is easier because
they do not match.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nguyen

Guest

Re: solving recurrence relations (checking ans)

Hi  Nguyen;

1) Is correct.

2) Is not correct. Your answer does not match the sequence the recurrence would generate.
Always check to see if the 2 match or prove your answer by induction. Here checking is easier because
they do not match.

Thank you bobbym.

Can you show me how 2 is done then?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solving recurrence relations (checking ans)

Hi;

Your method is fine, you have only found one root of the characteristic equation. Start there.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nguyen

Guest

Re: solving recurrence relations (checking ans)

Hi;

Your idea is fine, you have not found the correct roots to the characteristic equation. Start there.

Ah yes, silly me.

Which gives me

.

Correct?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: solving recurrence relations (checking ans)

Hi;

Yes, correct. Good work! Welcome to the forum.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.