sum of odd numbers
The sum of the first positive odd integers can be calculated by using the well-known of the arithmetic progression, that the sum of its is equal to the arithmetic mean of the first and the last , multiplied by the number of the :
Thus, the sum of the first odd numbers is (this result has been proved first time in 1575 by Francesco Maurolico).
Below, the odd numbers have been set to form a triangle, each row containing the next consecutive odd numbers. The arithmetic mean on the row is and the sum of its numbers is .
|Title||sum of odd numbers|
|Date of creation||2013-03-22 14:38:35|
|Last modified on||2013-03-22 14:38:35|
|Last modified by||pahio (2872)|