Page Three

     Sum of an Infinite Geometric Sequence
       where -1 < r < 1

             S∞ =  t1  
                   1 - r


Let's redo the two previous examples using this formula and a calculator:

Example 1:   16, 8, 4, ...
                   t1 = 16   r = ½

          S∞ =  t1  
                  1 - r

          S∞ =  16  
                  1 - ½

          S∞ = 32 		  Example 2:   27, -9, 3, ...
                   t1 = 27   r = -⅓

          S∞ =  t1  
                  1 - r

          S∞ =  27  
                  1 - -⅓

          S∞ = 20.5


Using this formula you can now easily and quickly find the sum
of any infinite geometric sequence where |r| < 1


A final example:

300, 30, 3, 0.3, ...    Find S∞

t1 = 300   r = 1/10

          S∞ =  t1  
                  1 - r

          S∞ =  300  
                  1 - 1/10

          S∞ = 333⅓


Page 1 | Page 2 | Page 3



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