Series notation and commutativity

[vorophobe]

Homework Statement

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:

Homework Equations

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

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?

 

[PeroK]

Actually, that is the definition of multiplication!

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

 

[Mark44]

Homework Statement

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:

Homework Equations

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

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?

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

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

 

[vorophobe]

Great replies thank you both!