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Question 73789This question is from textbook college algebra
: Im stumped!!! Is there an easy way to do these? Thanks so much!
Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
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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.
Answer:
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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.
Answer:
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d) What observation can make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
Answer:
This question is from textbook college algebra
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Starting with the sequence of: 1, 1/2, 1/4, 1/8,...
a) Find the common ratio.
The common ratio, r, is found by dividing any term by the preceeding term.
or
The common ratio is 1/2
b) The partial sum of the first n terms of a geometric series is given by:
 where:
 is the number of the term (1st, 2nd, 3rd,...)
 is the first term.
 is the common ratio.
To find the partial sum of the first 10 terms, set  ,  , . Substitute these values into the formula for the partial sum.
 To four decimal places.
You should be able to finish the other parts using the above as a guide.
If you have trouble with it, please re-post.
c) Find the partial sum of the first 12 terms.
For this part, n = 12 and we can use the same formula for the partial sum of the first n terms of a geometric sequence.
 To four deicimal places.
d) My observation is that the sum approaches 2.
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