- #1
EngWiPy
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Hello,
If we get a summation [tex]\sum_{r=a}^{b}[/tex], where a > b, how to treat this summation?
Regards
If we get a summation [tex]\sum_{r=a}^{b}[/tex], where a > b, how to treat this summation?
Regards
CRGreathouse said:Really? I'd interpret it as 0. That is, I take
[tex]\sum_{n=a}^bf(n)[/tex]
as shorthand for
[tex]\sum_{n\in\mathbb{Z},a\le n\le b}f(n)[/tex]
saeddawoud said:What is zero, the whole summation, or the index r?
Summation limits refer to the upper and lower bounds that determine the range of values to be included in a summation or series. These limits are denoted by the letters a and b, where a is the lower limit and b is the upper limit.
For summation limits, a is always the smaller value and b is the larger value. This means that a must be less than b for the summation to be valid. If a is greater than b, the summation will be considered as having no terms and will result in a value of 0.
Yes, a and b can be negative numbers for summation limits as long as a is the smaller value and b is the larger value. This means that the summation will include all values from a to b, including negative numbers, in ascending order.
If a and b are the same value, it means that there is only one term in the summation and the value of that term will be the result of the summation. This is because there are no values between a and b to be included in the summation.
Yes, a and b can be fractions or decimals for summation limits as long as a is the smaller value and b is the larger value. This means that the summation will include all values from a to b, including fractions and decimals, in ascending order.