Question 68835
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following:
a) 	What is r, the ratio between 2 consecutive terms? 
Answer:  
Show work in this space. 

To find "r", divide any term by the one before it.
r=1/3
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b) 	Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer: 
Show work in this space.   
S(10)=[(1/3)^11 - 1]/[(1/3)-1]
= 1.49999...
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c) 	Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:  
Show work in this space. 
S(12) = [(1/3)^13 - 1]/[(1/3)-1]
=1.499999...
  
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d) 	What observation can make about the successive partial sums of this series? In particular, what whole number does it appear that the sum will always be smaller than?

Smaller than 2
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Cheers,
Stan H.
Stan H.