An arithmetic series is the series, , in which each real term has the form for where is constant. The sum of the sequence is given by the following In order to find the formula above firstly we express the terms of the sequence, in terms of and the constant . In this case we get . Now we express the sum of the sequence by developing the series forward and we have:
Reversely, we develop the series backwards and we get
It is easily seen that by adding the two expressions we get
Hence, by substituting we get the first formula.
|Date of creation||2013-03-22 16:17:58|
|Last modified on||2013-03-22 16:17:58|
|Last modified by||georgiosl (7242)|