Question 83724
Use the geometric sequence of numbers 1, ½, ¼, 1/8,….to find the following: 

a) What is r, the ratio between 2 consecutive terms?
r = (1/2)/1 = 1/2
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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? Please round your answer to 4 decimals.
S(n) = a(1)[(r^(n+1)-1)/(r-1)
S(10) = 1[(1/2)^9-1] / [(1/2)-1]
S(10) = [-0.998046875...] / [-0.5] = 1.99609375...
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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? Please round your answer to 4 decimals.
Use the same formula with n=12.
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d) What observation can be made about these sums? In particular, what whole number does it appear that the sum will always be smaller than? 
Looks like it gets closer and closer to 2.
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Cheers,
Stan H.