Function triangleNumber

Function returns triangular number of passed size

Remarks

Triangular number equals to the sum of sequence of natural numbers from 1 to size n: $$ T_{n}=1+2+3+\dotsb +(n-1)+n $$

This function computes the triangular number of specified size by using very efficient implementation. It comes from basic mathematical definition of counting such sequences, as mathematically speaking, it is defined as binomial coefficient choosing number of distinct pairs from $ n+1 $ objects: $$ T_{n}=1+2+3+\dotsb +(n-1)+n={\frac {n(n+1)}{2}}={\frac {n^{2}+n}{2}}{\overset {\underset {\mathrm {def} }{}}{=}}{n+1 \choose 2} $$

Example

Simple use of finding triangular number:

import { triangleNumber } from 'simple-mathematic';

triangleNumber(1);        // 1
triangleNumber(2);        // 3
triangleNumber(5);        // 15
triangleNumber(1000);     // 500500
triangleNumber(Infinity); // Infinity
triangleNumber();         // NaN
triangleNumber(0);        // NaN
triangleNumber(-2);       // NaN
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