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I am working through a proof why determinants can be developed from any row or any column in a matrix. In passing, the authors claim that the summation $ \displaystyle \sum_{s=1}^{i-1}(\text{expression})$ has no values for $i=1$, since that would mean a sumnation from $1$ to $0$.

Is this a general rule for summations, that any summation with a lower value at the top and a higher value at the bottom is invalid?

I've never seen this mentioned anywhere else and it's typically not really mentioned in the definitions....

Alessio K
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Magnus
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    Yes. The convention for the $\Sigma$ notation for sums is that the step is $+1$. – Ethan Bolker Aug 29 '20 at 16:56
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    It is the convention used most of the time. However, it is not always used. The principal part of a Laurent series is often written $$\sum_{n = -1}^{-\infty} a_n z^n,.$$ – Daniel Fischer Aug 29 '20 at 17:52
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    Echoing other comments: it depends (on context). And one needs to be aware that often the usage is consistent with the convention/idea that an "empty sum" (no summands!?!) is $0$. – paul garrett Aug 29 '20 at 17:55

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