Conducted by BatStateU
, Started on 2013 -
Completed on 2014
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The nth triangular number, denoted by T (n), is defined as the sum of the first
consecutive positive integers. It can be represented in the form of a triangular grid of points. As
a result, this study discusses the triangular numbers and its properties. To distinguish whether a
positive integer N is a triangular number or not, it has to comply with 8N + 1 which is a perfect
square; characteristics of odd and even triangular numbers; sum of two consecutive triangular
numbers with same parity i.e., the formula for
2 T(4c 1) T(4c) (4c)
where c ≥ 1 and
2 T(4c 1) T(4c 2) (4c 2)
where c ≥ 0; and introduces the new figurative numbers through
deriving the formula of triangular number, Trapezoidal Number- an integer of
T(n) 1
, denoted
by T* (n)and Diamond Number- an integer of
2T(n) n
, denoted by D (n).