# Solving for a factor in a large sum

1. Dec 21, 2013

Dear everyone.

First of all Merry Xmas, when everybody gets to that.

I have a problem solving for a factor within a sum.

My formula looks as follows:

T = Æ© It * A0t

The sum runs from t=1 to N, and the aim is to solve for A0, but all my calculations end up extremely messy.

All the best,

Dan

2. Dec 21, 2013

### Kosomoko

What is It?

3. Dec 21, 2013

Thanks for the reponse.

That is the t'th observation of I. They have no well-defined relation to t. In other words; just a bunch of numbers.

4. Dec 21, 2013

### Kosomoko

In that case, your equation seems to be a general polynomial of order N. I guess N is probably fairly large (as in... not 2 or 3). You will need to use some numerical method to find roots of the function f(A0) = Æ© It * A0t - T.

I suggest Newton's method, it should be convenient to implement, because you can easily compute the derivative of the function analytically.

5. Dec 21, 2013

Actually it is not that large (N, that is), it is just that it varies a lot from case to case and hence I have written it as a sum.

Thanks so much for the response. I will try to see if it gets me any further!

6. Dec 21, 2013

And just to be clear. The A_0 has t as their exponent. It is not a subscript!

7. Dec 21, 2013

### scurty

If N is equal to 3 or 4, the polynomial is still solvable by analytic methods, but in general it is easier to use a numerical technique like Newton's Method (which is very easy to program if you choose to do that).

The N = 3 case isn't this bad, but consider the solutions for N = 4:

Of course, if you know $a$ is a solution to the polynomial, you can long divide by $(x-a)$ to reduce the degree by 1.