# Sigma notation and parentheses question

1. Jun 28, 2009

### Rib5

I have a question about sigma notation and parentheses. Does

$$\sum x[k] + x[n]$$

mean

$$\sum( x[k] + x[n])$$ or $$\left(\sum x[k] \right)+ x[n]$$

I find it a personal annoyance for things to be written with parentheses even if there are rules about it. Including parentheses would just reduce ambiguity. Another time I sometimes get confused is when trig functions are written without parentheses - grrrrrrr.

Last edited: Jun 28, 2009
2. Jun 28, 2009

Without more context I can see two possibilities.

a) It is $$\left( \sum_k x[k] \right) + x[n]$$

b) It is $$\sum_{k, n} (x[k] + x[n])$$

I think 'a' is the more reasonable, but I base that solely on a hunch. Is there more to the original article?

3. Jun 28, 2009

### Rib5

I worked out the problem it was in and it was in fact 'a'. I'm wondering if there is some rule or if you just have to look and sorta figure it out based on the context?

Last edited: Jun 28, 2009
4. Jun 28, 2009

### HallsofIvy

Staff Emeritus
It is probably (a) but parentheses surely should have been used!

5. Jun 28, 2009

My clue for going with 'a' as my most likely choice was the single summation symbol but $$x$$ occurring twice with different indices.

It was an incredibly poorly written expression - in what context was it (math, physics,?)

6. Jun 29, 2009

### Rib5

Don't know if you still care, but it was in my electrical engineering signals and systems book. The book was pretty much talking about how it is possible to rewrite a sum as the sum up to a certain number by the sum up to that last (number - 1) with the final value of the signal added. This was in discreet time obviously. It seems really obvious when I state it here, but in the book they jumped a few steps which made it even harder to figure out what that equation was saying.

7. Jun 29, 2009