# Properties of summation

1. Feb 7, 2010

### dE_logics

If I have ∑(k xi + j yi)...how will I apply the distributive law on it?...I mean how do you split this notion?

2. Feb 7, 2010

### tiny-tim

Hi dE_logics!

∑(k xi + j yi)

= ∑(k xi) + ∑(j yi)

= k ∑(xi) + j ∑(yi)

(if the ∑ is over infinitely many terms, you may have to be careful about convergence …

but if for example all the terms are positive, then there's no difficulty )

3. Feb 7, 2010

### dE_logics

So we wont get ∑(k xi) + ∑(j yi)...that was too a possibility.

So let's take an e.g. -

x1 = 1, x2 = 2, x3 = 7, x4 = 1
y1 - 19, y2 = 8, y3 = -10, y4 = 0
k = j= 3

∑(k xi + j yi) gives -30

k ∑(xi) + j ∑(yi) = -30

and

∑(k xi) + ∑(j yi) = -30

So both of the solutions are true...does everyone agree?...I mean -

∑(k xi) + ∑(j yi) = k ∑(xi) + j ∑(yi)

4. Feb 7, 2010

### HallsofIvy

??Yes, we will, that was Tiny-tim's first step! But you asked about the distributive law and that hasn't been used yet, so then he factored k and j out.

Yes, of course.

5. Feb 7, 2010

### dE_logics

Oh...I didn't see that...thanks.