sum of odd numbers

The sum of the first n positive odd integers can be calculated by using the well-known of the arithmetic progressionPlanetmathPlanetmath, that the sum of its is equal to the arithmetic meanMathworldPlanetmath of the first and the last , multiplied by the number of the :


Thus, the sum of the first n odd numbersMathworldPlanetmath is n2 (this result has been proved first time in 1575 by Francesco Maurolico).

Below, the odd numbers have been set to form a triangle, each nth row containing the next n consecutive odd numbers.  The arithmetic mean on the row is n2 and the sum of its numbers is  nn2=n3.

Title sum of odd numbers
Canonical name SumOfOddNumbers
Date of creation 2013-03-22 14:38:35
Last modified on 2013-03-22 14:38:35
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 15
Author pahio (2872)
Entry type Example
Classification msc 00A05
Classification msc 11B25
Related topic NumberOdd