Combination and summation notation.

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SUMMARY

The discussion focuses on understanding combination and summation notation, specifically the expression \(\sum (i/k)\) from \(i=0\) to \(n\). The user is confused about how to represent combinations in programming and how to handle cases where \(n < k\) in the context of the combination formula \(n!/(k!(n-k)!)\). It is established that when \(n < k\), the combination is undefined, as negative factorials are not valid.

PREREQUISITES
  • Understanding of summation notation and its limits
  • Familiarity with the combination formula \(n!/(k!(n-k)!)\)
  • Basic programming skills for implementing mathematical formulas
  • Knowledge of factorial properties and their constraints
NEXT STEPS
  • Research how to implement summation notation in programming languages like Python
  • Learn about handling edge cases in combinatorial functions
  • Explore mathematical libraries that can compute combinations and factorials
  • Study the implications of negative values in factorial calculations
USEFUL FOR

Students in mathematics, computer science majors, and anyone involved in programming combinatorial algorithms will benefit from this discussion.

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Homework Statement


I am having trouble reading this notation

[tex]\sum[/tex] (i/k)

The sum is from i=0 to n

I wasn't sure how to write the combination of i,k on the computer so I just wrote it as i/k.


Homework Equations


When I say combination I am talking about this formula n!/(k!(n-k)!)


The Attempt at a Solution



Is this just (0/k)+(1/k)+(2/k)...(n/k)

I am sure I am interpeting it wrong but If I am not what do you do for situations where n is less than k because when you do the combination you get n!/(k!(n-k)!), and I don't think it is possible to do a negative factorial.
 
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I don't think 'n' can be less than 'k' for the reason you said.
 

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