It is well known that a finite geometric series is given by
where in general is complex. When we are dealing with such sums it is common to consider the expression
which we shall call an arithmetic-geometric series. Let us derive a formula for .
We will proceed to eliminate the right-hand side sums.
By using (1) and solving for , we obtain
This last result giving the sum of a converging arithmetic-geometric series may be, naturally, obtained also from the sum formula of the converging geometric series, i.e.
when one differentiates both sides with respect to and then multiplies them by :
|Date of creation||2013-03-22 16:02:15|
|Last modified on||2013-03-22 16:02:15|
|Last modified by||perucho (2192)|