Question 26308: 3) Use the geometric series of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
b) Using the formula for the nth term of a geometric series, what is 10th term? Answer:
Show work in this space.
c) Using the formula for the nth term of a geometric series, what is 12th term? Answer:
Show work in this space.
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a) r=(1/2)/1=1/2
b) 10th term = (1st term)(1/2)^(10-1)
= (1/2)^9 = 1/512
c) 12th term = (1st term)(1/2)^11
= 1/2048
d) Each term is (1/2) the term before it. The sum of
the terms up to any point will be less than 2.
Cheers,
Stan H.
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