Sigma Notation: Definition and Examples

AI Thread Summary
The discussion revolves around the interpretation of a specific sigma notation involving a block defined by a contiguity condition. Participants express confusion over the ambiguity of the notation, particularly regarding the role of "n" and its implications for the set S. One interpretation suggests calculating the function f(c) for all elements c in set S that are less than or equal to n before summing them. The need for context around the notation is highlighted, as it is unclear without knowing the actual function being referenced. Overall, clarity on the definition and application of the notation is essential for proper understanding.
bitttttor
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What does this mean? (see attachment)

"Where b is a block defined by the contiguity condition c that may exist between elements of s, and n is the number of elements in that block"

I know is not possible to get a solution without the actual function, but how does this reads?
 

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That notation is a little ambiguous. Just
\sum_{c\in S} f(c)
would mean "caclulate f(c) for all c contained in set S, then add". But the "n" is problematic- the set S, in general, doesn't even have to be a set of numbers.

My best guest would be "calculate f(c) for all c contained in set S, that are less than or equal to n, then add them."
 
Great, thank you.
 
bitttttor, are you able to say more about the background to this? In what context did you find it?
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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