Question 26075: 10) 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?
b) Using the formula for the nth term of a geometric series, what is 10th term?
c) Using the formula for the nth term of a geometric series, what is 12th term?
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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?
R=(1/2)/1=1/2...IT IS SAME FOR ANY 2 CONSECUTIVE TERMS...SAY
(1/8)/(1/4)=1/2...ETC......
b) Using the formula for the nth term of a geometric series, what is 10th term?
TN=A*(R)^(N-1)=1*(1/2)^(N-1)
T10=(1/2)^(10-1)=(1/2)^9
c) Using the formula for the nth term of a geometric series, what is 12th term?
T12=(1/2)^11
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
THE NUMBERS TEND TO ZERO AS N INCREASES TO LARGE NUMBERS AND TOWARDS INFINITY.
SUM OF A G.P. TO INFINITE TERMS WITH R<1 IS GIVEN BY
A/(1-R)=1/(1-0.5)=2
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