# Series notation and commutativity

1. Nov 21, 2013

### vorophobe

1. The problem statement, all variables and given/known data
I'm trying to wrap my head around series notation, but I'm finding some of the transformations hard to grasp. For example, this one:

2. Relevant equations
$\Sigma^{n}_{i=1} (2a_{i}-3) = 2\Sigma^{n}_{i=1}a{_i}(-3n)$

3. The attempt at a solution
In the above expression, I don't understand how you end up with -3n on the RHS. Why can't it just be left as -3?

2. Nov 21, 2013

### PeroK

Actually, that is the definition of multiplication!

$3n = \overbrace{3 + 3 + ... + 3}^{n \ times} \ = \ \sum_{i=1}^n3$

3. Nov 21, 2013

### Staff: Mentor

$\sum_{i = 1}^n (2a_i - 3) = \sum_{i = 1}^n 2a_i - \sum_{i = 1}^n 3$

The last sum is 3 + 3 + 3 + ... + 3, a sum with n terms.

4. Nov 21, 2013

### vorophobe

Great replies thank you both!