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Основы программирования и алгоритмы

Triangular Number

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Lambert M. S.    
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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. A triangular number is the number of dots in an equilateral triangle evenly filled with dots. The nth triangle number is the number of dots in a triangle with n dots on a side. High Quality Content by WIKIPEDIA articles! 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. For example, three dots can be arranged in a triangle; thus three is a triangle number.
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