SOLUTION: Can someone help me with this? Thank you.
infinite geometric series a+ar+ar^2+ar^3+... converges to 10, and the terms involving the even powers of r converges to 6. What is the v
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-> SOLUTION: Can someone help me with this? Thank you.
infinite geometric series a+ar+ar^2+ar^3+... converges to 10, and the terms involving the even powers of r converges to 6. What is the v
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Question 1112961: Can someone help me with this? Thank you.
infinite geometric series a+ar+ar^2+ar^3+... converges to 10, and the terms involving the even powers of r converges to 6. What is the value of a+r? Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! infinite geometric series a+ar+ar^2+ar^3+... can be written
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summation from k = 0 to infinity of ar^k, since it converges we can write
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1) a/(1-r) = 10
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since the above series begins at k=0, I assume the series of even powers begins at k=0 also
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summation from k = 0 to infinity of ar^(2k), since it converges we can write
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2) a/(1-r^2) = 6
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solve equation 1 for a
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a = 10(1-r)
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substitute for a in equation 2
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10(1-r)/(1-r^2) = 6
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(1-r)/(1-r)(1+r) = 6/10
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1/(1+r) = 3/5
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cross multiply the fractions
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5 = 3 +3r
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r = 2/3
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a = 10(1-(2/3)) = 10/3
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(10/3) + (2/3) = 12/3 = 4
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