# OT math help.

Discussion in 'Electronic Basics' started by George Herold, Dec 18, 2013.

1. ### George HeroldGuest

Hi all, I was helping my daughter with algebra last night.
One set of problems had you find the generating function for a list of integers.
For instance,
list was 1,4,16,64...
Which I wrote as F(n) = 4*F(n-1), F(1) = 1
The HW started counting at n=1 rather than zero... but that hardly matters.
Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.
F(n) = 4^(n-1).
But it seems there should be a more formal way to arrive at the answer.
So what is it?
A solution for the above would be fine... or web link, or just tell me what this type of problem is called and I can go find the answer on my own.

Thanks George (and Elsie) H.

2. ### George HeroldGuest

Thanks Jim, that helps. After posting the question I went and 'guessed' a solution but with unknown coefficients, and then plugged the guess back into the
formula and 'found' the coef. So that at least works. The math 'savy' comes in making a good guess!

Is it correct to think of these types of problems as a 'digital' form of a differential equation?

George H.

3. ### George HeroldGuest

Phil, do you every get the feeling that you're too smart for your own good?
(He asked with a smile on his face.)

Did you miss the three little dots? 16,64... so 256, 1024... (etc.)

So given F(n) = 4*F(n-1) and F(1) = 1, is making a good guess the best way to get to a solution? (with unknown coefficients.)

George H.

4. ### George HeroldGuest

Fun, I never heard of pedagogue. Hmm if I tell her math teacher I hear she's a good pedagogue will I be slapped?

5. ### Jasen BettsGuest

The "easy" way to automate it is to find a polynomial
solution by means on simultaneousl equations.

That won't find 4^(n-1) but something else that fits those points.

the other way is to type them into google, with quotes around them
you'll get a result from OEIS

I remeber being given sequences like this 4,3,3,5,4,4,3,5,5,4,3,6,6,8
or 7,8,4,5,3,4,4 in highschool.. I suspect these where put on the end keep the
fast students quiet.

6. ### George HeroldGuest

Feeling chastised.
Lowers head, kicks dirt with shoe, "Sorry guys".

(I just hope they don't see the little smirk on my face :^)

George H.