Triangular Numbers in Quadratic Functions Form, Generating Functions and Continued Fractions
Abstract
The triangular number denoted by Tn is defined as the sum of the first consecutive positive integers, and a positive integer is a triangular number if and only if Tn= n(n+1)/2. In this paper we represent a triangular number by a quadratic function i.e., for each m the necessary and sufficient condition for a quadratic function f(x)= x2 +x - 2m to be triangular is proved. We also prove, a theorem associated to a rational root d of a quadratic function f(x) to be a triangular number Tn. We also use Generating function to represent the sets of Quotients of triangular numbers.
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References
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