Question 39011: Don't know how to do these. Please help.
3) 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.
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 7 significant figures.
Answer:
Show work in this space.
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 7 significant figures.
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! 3) 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.
r = [1/3]/1= 1/3
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 7 significant figures.
Answer:
Show work in this space.
S(10)=[r^10-1]/[r-1]= [(1/3)^10-1]/[1/3 - 1]
=-0.99998306.../(-2/3)1.49997460...
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 7 significant figures.
Answer:
Show work in this space.
S(12)=[(1/3)^12 - 1]/[(1/3)-1]= -0.99999812.../(-2/3)
=1.49999718...
d) What observation can you make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
I'll leave this to you.
Cheers,
Stan H.
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