# Thread: How would you minimize this sum?

1. ## How would you minimize this sum?

$\sum_{i=1}^{n-1} \sqrt{(a+b)^2}$

2. ## Re: How would you minimize this sum?

Originally Posted by MathIsOhSoHard
$\sum_{i=1}^{n-1} \sqrt{(a+b)^2}$
What does that question mean?
What are $a~\&~b~?$

3. ## Re: How would you minimize this sum?

Originally Posted by Plato
What does that question mean?
What are $a~\&~b~?$
a and b are just random constants. I would like to minimize the sum the way they explain it at the bottom of this page:
Sum -- from Wolfram MathWorld

4. ## Re: How would you minimize this sum?

What you have shown is simply $(n- 1)|a+b|$. You can minimize that by taking, for example, any value for a and then taking b= -a.

Surely that's NOT what you intended to say.

Notice that in the example you link to, the sum is over the index i and there is a $x_i$ in the summand so you have different terms for different i in your sum. Your example does not have that. I don't think anyone can answer what you meant to ask until you clarify what you are asking.