I would like to know what's the standard way to say sequential/continuous/continued/parallel multiplication or addition for calculation like `3 * 5 * 10 * 2 * 11` and `1 + 5 + 3 + 2 + 4 + 100`.

PS: Glad that this question attracts some attention. I asked because in Chinese there are effectively specific names: `连加` and `连乘` where `连` means this, `加` means addition and `乘` means mutiplication.

• The sum of a sequence is called a 'series', usually referring to the (a + b + c + ...) form rather than the actual total. But sequences are patterned rather than being repeated addition operations with arbitrary terms. Commented Apr 6, 2021 at 13:57
• I’m sure this is a better fit on Mathematics.SE. Commented Apr 6, 2021 at 13:59
• [correction: I would like to know the standard way to say: blah blah blah] Commented Apr 6, 2021 at 14:23
• @lambie there is no rule telling you that you have to use a colon after the object, and you told me that this is not the point, yet you do add one; why not write "I would like to know the standard way to say blah blah blah"?
– LPH
Commented Apr 6, 2021 at 16:02
• @LPH I was not correcting the colon: I was correcting the grammar. Did you miss the grammar? Commented Apr 6, 2021 at 16:06

Such calculations don't have a specific name. They are merely products or sums (respectively). The answers which suggest, for example, that you refer to the sum as a series are incorrect, as the relevant feature to create a series appears to be missing. You would need to identify a relationship between elements of the series, specifically a way to calculate each successive element, and the sequence of values (typically integers) over which to perform the calculation.

To be clear, it's not that it's impossible to create such a calculation, it's that you've not provided the relationships, and one is not readily apparent. There may be a function, the sequence of which would result in the elements of your sum or product. But it's not given, and it's not obvious.

• You do not have to provide a rule of calculation of the terms; all you need is a function and any function with a finite domain and range such as those involved here can be specified by the set of its ordered pairs. For instance: f(1)=1, f(2)=5, f(3)=3, f(4)=2, f(5)=4, f(6)=100; then ∑f(x) is a defined finite sum (we don't say "series" usually, although it is possible. On the contrary, the function is obvious. I agree with you, however, on this point: terms such as "iterated sum" are not used often (math.stackexchange.com/questions/182704/…).
– LPH
Commented Apr 6, 2021 at 16:46

From this source, where the symbol "∑" is said to represent an iteration, you could call expressions such as "1 + 5 + 3 + 2 + 4 + 100" iterated sums (similarly for products).

You can also speak of repeated sums (Notation) (similarly for products).

• I believe this answer isn't correct. The idea behind iterated elements for such sums is that one is able to identify a function which creates successive elements. No such function is provided here, nor is one apparent. Commented Apr 6, 2021 at 16:08
• Even if there exists some function f that generates 1, 5, 3, 2, 4, and 100, describing their sum as an "iterated sum" lacks clarity. ∑f(x) represents a sum of iterations of f(x). "Iterated sum" better describes an operation of the form ∑∑f(.) where the sum itself is being iterated. Commented Apr 6, 2021 at 18:43
• @DerrellDurrett There is always an index set and in fact any set of the same cardinal as the set of terms of the sum paired with 1, 2, 3, …will do, the simplest being a segment of the natural numbers starting at 0 or 1; but you can use any set and construct a function. There exists in fact an infinity of functions having the range {1,5,3,2,4,100}; it is only needed to choose as domains (which will be the index sets) the sets {1,2,3,4,5,6}, {2,3,4,5,6,7},{3,4,5,6,7,8}, etc. They can all be an index set for the sum "1 + 5 + 3 + 2 + 4 + 100".
– LPH
Commented Apr 6, 2021 at 19:11
• @max norton Your specialization to sums of sums is probably not a general practice. Here is what Wikipedia says of iterated binary operations: "In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation.
– LPH
Commented Apr 6, 2021 at 19:12
• @LPH But the sentences you have cited also imply that summation can be defined as iterated addition, with the result that iterated summation is either redundant or means the iteration of the summation operation. The math stack exchange post you linked to in a different comment uses "iterated sums" in the way I'm suggesting, to refer to ∑∑f(.). Commented Apr 6, 2021 at 20:35

These are just sums and products, both of which are neutral with respect to the number of elements they operate on. (Reference: The first definition of sum in the American Heritage Dictionary, 5th ed. is, "An amount obtained as a result of adding numbers.")

One plain-language option that hasn't been raised is that if you have a word to describe the set of numbers you're operating on, then you can talk about the sum of all or product of all elements in the set, e.g.,

The sum of all the passengers' weights should not exceed the elevator's weight capacity.