Triangular Number

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The nth triangle number is the number of dots in a triangle with n dots on a side. The rightmost term in the formula, consisting of the two numbers n + 1 and 2 on top of each other within parentheses, is the standard mathematical notation for a binomial coefficient that counts the number of distinct pairs to be selected from n + 1 objects. In this form the triangular number Tn solves the "handshake problem" of counting the number of handshakes if each person in a room full of n + 1 total people shakes hands once with each other person.