Find the sum of the first six terms of the geometric sequence 1/2, 1/6, 1/18, ... Express your answer as a common fraction.
Sum =
first term [ 1 - common ratio ^n ] / [ 1 -common ratio]
Where
first term 1/2
common ratio = 1/3
n = the number of summed terms
So
(1/2) [ 1 - (1/3)^6] / [ 1 -1/3 ] =
(3/4) [ 1 - (1/3)^6] =
182 / 243
