What do three dots #...# mean in sequences?

1 Answer
Jun 13, 2017

Ellipsis dots are used in place of terms not listed.

Explanation:

When used at the end of a list, the ellipsis usually means that the sequence continues indefinitely.

For example:

#1, 2, 3,...#

indicates the sequence of positive integers in ascending order.

Note the assumption that the pattern of the sequence is understood. If you wanted to indicate the sequence of triangular numbers, then you might write:

#1, 3, 6, 10, 15,...#

When used in the middle of a list, the ellipsis stands for terms not listed, but which follow the pattern.

For example:

#2, 4, 6,..., 100#

indicates the list of even numbers from #2# to #100#.

If you want to make the pattern explicit, you might write something like:

#2, 4, 6,..., (2n),..., 100#

Going back to our list of triangular numbers, we might choose to write:

#1, 3, 6, 10,..., (1/2n(n+1)), ...#

indicating that the #n#th term is given by the formula:

#a_n = 1/2n(n+1)#