# Summation problem

1. May 20, 2014

### lilly92

1. The problem statement, all variables and given/known data
I have an equation in the general form:
const=b*∑i2yi+∑f(I)f(y).....)
where const,b are known constants.I have a general question.Is it possible from equations like this to identify how the ys should be distributes so as the const takes a specific value, e.g const=0.05? What I thought of doing was to assume that const is a radius of convergence but the sums are finite (n=20000 at most). A few general pointers would be greatly appreciated or if this is even solvable.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 20, 2014

### dirk_mec1

3. May 20, 2014

### lilly92

clarification

OK let me try and explain it a little better. I know that const takes a specific value, i.e. const=0.05. I need to find what the "arrangement" of yis must be for this to happen. Think of it as follows: If y are a set of data values in what order should these values appear for the right part of the equation to converge to 0.05(what their distribution should be)?Is it even possible to do sth like this?

4. May 20, 2014

### Ray Vickson

Do you have an equation of the form
$$0.05 = b \sum_{i=1}^n i^2 y_i + \sum_{i=1}^n f(i) g_i(y_1,y_2, \ldots, y_n)$$
with known functions #f# and $g_i$? That SEEMS to be what you are asking, but in very poor notation. If you mean something else, please try first to put it in good notation and not to leave out important information.

5. May 20, 2014

### lilly92

Yes, that's what I mean. I apologise.I didn't think the exact equation was necessary because I'm looking for some general pointers or even a yes-or-no answer if what I'm trying to do can be done. Thank you for your time.