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April 13th, 2012, 04:12 AM   #1
Ter
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Geometric Progression

Hello World,

I am urgently looking for solutions to these questions. Would appreciate the help!

10 15
1.)Prove that a.) ? 8(0.5)^n and b.) ? 2-(5^(-n)) is geometric and find each sum.
n=1 n=1
How do you prove that it is geometric and I think I know how to find each sum, if proving that the series is geometric gives me the common ratio.

2.) Nine numbers are in GP and are alternately positive and negative. If the first number is 24 and the last number is 3/32, find the sum of the numbers.

I got U1 = 24 and ar^8 = 3/32
Therefore, r^8 = (3/32)/(24) and I got 1/256
Since it is alternately positive and negative, I believe the common ratio should be a negative.
But then how do I continue, or am I even doing it right?

100
3.) Evaluate ? (0.01n+0.09^n)

Thank you much!
n=1
Ter is offline  
 
April 13th, 2012, 04:48 AM   #2
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Re: Geometric Progression

1. Use the definition of a geometric serie.
2. What you have done so far is correct, note that , but indeed because you have an alternating sequence
From this point, you should be able to find the sum of the numbers.
3.
Note that you have a sum that means you can split the summation as:


The first summation is an arithmetic serie and the second is a geometric serie.
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April 13th, 2012, 05:34 AM   #3
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Re: Geometric Progression

Hello, Ter!

Quote:
















Quote:










soroban is offline  
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