a1. The nth triangular number is the sum of the numbers from 1 to n. The sequence goes 1, 3, 6,10, 15, 21, 28, ... At this point, they won't have a formula for the nth triangular number, just a procedure for finding it. 1. 第n个三角数字是数字的总和从1到n。 序列去1, ...
Another way to think of this is that these are triangular numbers, and we can see how we can calculate the answer by copying, rotating, and making a rectangle N×(N+1), half of which is the solution.The sum of the numbers 1–N is N(N+1)/2...
The article presents the formula for the triangular number of natural numbers' sum and product. It examines the properties of the triangular number fraction. It points out that a simple algebraic argument shows the pattern extending the triangular number of a sum of an arbitrary number of numbers...
tetrahedral numbersfigurate numbersThis note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of r natural numbers. The formula is applied to derive formula for the sum of an odd ...
2.: We can calculate the first 10 terms using the formula for triangular numbers: - - - - - - - - - -T10=10(10+1)2=55 Thus, the first 10 terms are: 1,3,6,10,15,21,28,36,45,55 3.Calculate the Sum of the First 10 Terms: We can sum these terms: ...
We also find generating function formulae for various subsequences of { s(n) }, for instance MD Hirschhorn,JA Sellers,C College - 《Discrete Mathematics》 被引量: 101发表: 1999年 On the representation of integers as sums of triangular numbers In this survey article we discuss the problem of...
andthe Bernoulli numbersBnare the values of the Bernoulli polynomials atX=0; that isBn:=Bn(0)(∀n∈N). To make the difference between the Bernoulli polynomials and the Bernoulli numbers, we always put the indeterminateXin evidence when it comes to polynomials. Similarly,the Euler polynomialsEn...
Consider the zero-field Ising model for a two-dimensional triangular lattice. Using blocks of three spins, establish an approximate form of the renormalization transformations, and evaluate the thermal-like critical parameters of the model. The Ising model on a triangular lattice is schematically indic...
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BK Oh,ZW Sun - 《Journal of Number Theory》 被引量: 68发表: 2005年 On the Representation of Natural Numbers as Sums of Squares. Presents the mathematical formula on the representation of natural numbers as sums of squares of nonnegative integers. Assessment of mathematicians; Theori... Panai...