The empty sum is such a borderline case of sum where the number of the addends is zero, i.e. the set of the addends is an empty set.
In using the sigma notation (http://planetmath.org/Summing)
one sometimes sees a case
It must be an empty sum, because in
the number of addends is clearly one and therefore in (2) the number is zero. Thus the value of (2) may be defined to be 0.
Note. The sum (1) is not defined when is less than , but if one would want that the usual rule
would be true also in such a cases, then one has to define
because by (4) one could calculate
|Date of creation||2013-03-22 18:40:57|
|Last modified on||2013-03-22 18:40:57|
|Last modified by||pahio (2872)|