Question 34042
1, 1/2, 1/4, 1/8,…
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<font color=blue>What is r, the ratio between 2 consecutive terms?</font>
second term=1/2
third term=1/4
ratio r=third/second=(1/4)/(1/2)=<B>(1/2)</b>
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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. 
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a=1,n=10,r=0.5
sum for n terms={{{a(1-r^n)/(1-r)}}}
={{{(1)(1-(0.5)^n)/(1-0.5)}}}
={{{(1-(0.5)^n)/(0.5)}}}
={{{(1-0.0009765625)/0.5}}}
={{{0.9990234375/0.5}}}
=1.998046875
=1.9980(rounding off)
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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. 
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a=1,n=12,r=0.5
sum for n terms={{{a(1-r^n)/(1-r)}}}
={{{(1)(1-(0.5)^n)/(1-0.5)}}}
={{{(1-(0.5)^n)/(0.5)}}}
={{{(1-(0.5)^12)/(0.5)}}}
={{{(1-0.000244140625)/0.5}}}
={{{0.999755859375/0.5}}}
=1.99951171875
=1.9995(rounding off)
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What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?</font>
The number will approach 2.
It will reach 1.999999999999999999999999....upto infinity, but it will always be smaller than 2
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Hope this helps,
-xC