# Thread: A recursive relation table and proving problem...

1. ## A recursive relation table and proving problem...

Hello

Given this:
an = a(n-1) - 1/4A(n-2)
Where n is an element of N (any whole number, 0,1,2,3...)

a1 = a2 = 1

Create a table with A1, A2, A3, A4, A5 and their answers.

Then prove that the explicit formula is:
An = n(1/2)^n-1

My shot at it:
The thing that I am stumped on:
a1 = a2 = 1
Does this mean that for all N's the answer is 1?
a3 = a(n-1) - 1/4A(n-2)
a3 = a2 - 1/4*a1, a3 = 1 - 1/4*1 = 0.25???

2. a3 = a2 - 1/4*a1, a3 = 1 - 1/4*1 = 0.25???
Correct, (ignoring that you put a 0.25 instead of 1 0.75)

3. The prize for doing math at 6 am after a night in the C++ language.
1-0.25 = 0.75!

Thanks a ton, but how do I prove or not prove that the formula can be written as:
An = n(1/2)^n-1?

I mean, doing so leaves me with the same answers... so the formula is correct, but proving it???
Of course I could write it with words, explaninig why, but that does not prove it? hmm...

4. Just show that that formula satisfies the given recursive relation. If it has the correct values at n= 1 and 2 and satisfies the relation, then it is a correct solution. That's what "solution" means!

5. Alright, consider it done!