Hence, the triangular number
can reduce the information distortion and information deviation in the process of decision-making.
Hence a triangular number
(a1; aM; a2) can be written in the form of a trapezoidal number, i.
Proof: (i) ([right arrow]) Assume T is a triangular number
2] Triangular numbers
[ILLUSTRATION OMITTED] 1 1 3 1 + 2 6 1 + 2 + 3 10 1 + 2 + 3 + 4 15 1 + 2 + 3 + 4 + 5 .
It is a reasonably well-known fact that the sum of consecutive cubes is the square of the corresponding triangular number
, that is
Were they able to articulate the relationship between a triangular number
and its position in the sequence?
Proof: T is a perfect number [&&] T is a triangular number
For example, students might try to determine the maximum number of iterations, or repetitions, needed to reach the marching group for a given triangular number
of seeds distributed among consecutive holes.
Note that the first triangular number
is associated with the fictitious triangle of side length zero units.
Each subsequent number in the triangular number
sequence is created by adding a row to the bottom of the triangle.
while the other Smarandache sequences of triangular numbers
only show, among the first 1000 terms, the trival triangular number
Using the sum of an arithmetic progression with common difference 1, it can be shown that the nth triangular number
is given by