What Does the Limit of Summation i<j Mean?

In summary, the notation "i<j" in the limits of summation indicates that the summation is only performed for values of i that are less than j. This can be thought of as a conditional statement, where the summation is only executed if the condition of "i<j" is met. Both "i<j" and "j>i" can be used interchangeably to represent this range of values. The value of j is not included in the summation when using "i<j" as the upper limit is used as a boundary. However, "i<=j" can also be used to include j in the summation, although this may affect the overall value of the summation.
  • #1
AKBAR
5
0
Hi,

I'm having some trouble understanding what is meant when the limit of a summation is i<j. Does it mean the limits are i = 0 to i = j?

Thanks!
 
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  • #2
If i is always strictly less than j, then index i's maximal value is j-1.
 
  • #3


Hello,

The limits of summation i<j means that the summation is only being performed for values of i that are less than j. For example, if the summation is written as Σi<j, then the summation would only be performed for i = 0, 1, 2, ..., j-1. This is also known as a "restricted summation" where the range of values for i is limited to be less than j.

I hope this helps clarify the concept for you. If you need further assistance, please don't hesitate to ask.
 

1. What does the notation "i

The notation "i

2. How do I interpret the limits of summation "i

When "i

3. Can the limits of summation "ii"?

Yes, the limits of summation "ii". Both notations indicate that the summation is limited to a specific range of values for i, starting from the lower limit and ending at the upper limit.

4. Do the limits of summation "i

No, the value of j is not included in the summation when using the limits of summation "i

5. Can the limits of summation "i

Yes, the limits of summation "i

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