The series obtained by adding the terms of a G.P. is called the geometric series. Let be the sum of the first terms of the G.P. The  term is , the  term is , etc. Hence
                           --- (1)
            Multiplying both members of (1) by , we get
                         --- (2)
            On subtracting each side of (2) from the corresponding side of (1), we obtain
                                     
                                   
                               
If the common ratio in a G.P. is more than, then each successive term is greater than the previous one and the sum of the terms grows very rapidly and tends to an infinity as  tends to infinity.
            If the common ratio is less than, then each term will be smaller than the previous one and the total will increase but will not exceed a finite value as  tends to an infinity. Thus
                                   

Example:
            Using G.P., find the sum of .
Solution:
                                  We have
            ,  and
            Substituting these values in the given formula, we get
                               (as)
                       

Example:
            Given, , , find .
Solution:
            Since,