SOLUTION: Write the series in summation notation and find the sum 6+2+(2/3)+(2/9)+...+(2/729)

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Question 1137523: Write the series in summation notation and find the sum
6+2+(2/3)+(2/9)+...+(2/729)
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is 6*(1/3)^n, where n runs from 0 to 6. Sum n=0 to 6 of 6*(1/3)^n
the terms are 6
2
2/3
2/9
2/27
2/81
2/243
2/729
sum of 7 =a(1-(1/3)^8)/(1-(1/3))
This is 6*(1-1/6561)/(2/3)
This is 9(1-1/6561)
or 9-9/6561
This is 9-3/2187 which is the same as 8+2184/2187

8+2/3+...
8+(1458/2187)+(486/2187)+(162/2187)+(54/2187)+(18/2187)+(6/2187)
8+(2184/2187) ANSWER