Sigma notation and parentheses question

In summary, there is an equation that can be rewritten to sum up to a certain number by the sum up to that last (number - 1) with the final value of the signal added.
  • #1
Rib5
59
0
I have a question about sigma notation and parentheses. Does

[tex]\sum x[k] + x[n][/tex]

mean

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

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.
 
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  • #2
Without more context I can see two possibilities.

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

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

I think 'a' is the more reasonable, but I base that solely on a hunch. Is there more to the original article?
 
  • #3
statdad said:
Without more context I can see two possibilities.

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

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

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

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 sort of figure it out based on the context?
 
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  • #4
It is probably (a) but parentheses surely should have been used!
 
  • #5
My clue for going with 'a' as my most likely choice was the single summation symbol but [tex] x [/tex] occurring twice with different indices.

It was an incredibly poorly written expression - in what context was it (math, physics,?)
 
  • #6
statdad said:
My clue for going with 'a' as my most likely choice was the single summation symbol but [tex] x [/tex] occurring twice with different indices.

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

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
Thanks. You will find poorly formatted items in texts and articles from almost every discipline, but that is little consolation when you have to make an attempt to decode the author's (or authors', if multiple) carelessness.
 
  • #8
statdad said:
Thanks. You will find poorly formatted items in texts and articles from almost every discipline, but that is little consolation when you have to make an attempt to decode the author's (or authors', if multiple) carelessness.

This actually is a little consolation because I heard that electrical engineers are especially bad about not using rigorous mathematics and using lots of shortcuts. I hope notation is not one of those.
 

What is sigma notation?

Sigma notation is a mathematical shorthand notation used to represent the sum of a sequence of numbers. It is represented by the symbol Σ (the Greek letter sigma) and an expression written below it, with the index variable specified on the bottom and the starting value indicated on top.

How do I use sigma notation?

To use sigma notation, you need to first identify the index variable, the starting value, and the ending value of the sequence. Then, you plug in the index variable into the expression and sum up the values as you increment the index variable from the starting value to the ending value.

What are parentheses used for in sigma notation?

Parentheses are used in sigma notation to indicate the order of operations for the expression within them. This is important when the expression contains multiple operations, such as multiplication and division, as it ensures the correct calculation is performed.

Can I use sigma notation for any type of sequence?

Yes, sigma notation can be used for any type of sequence, including arithmetic, geometric, and even more complex sequences. As long as you can identify the index variable, the starting value, and the ending value, you can use sigma notation to represent the sum of the sequence.

Is there an easier way to represent a long sum using sigma notation?

Yes, you can use the shortcut notation for sigma notation, which starts with the starting value and ends with the ending value, with the expression written after the sigma symbol. This indicates that the index variable increments by 1 each time. For example, instead of writing Σ(i=1 to 100) 2i, you can write Σ100 2i.

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