document.write( "Question 1112961: Can someone help me with this? Thank you.
\n" ); document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #728006 by rothauserc(4718) $\"\"$ $\"About$

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infinite geometric series a+ar+ar^2+ar^3+... can be written
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\n" ); document.write( "summation from k = 0 to infinity of ar^k, since it converges we can write
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\n" ); document.write( "1) a/(1-r) = 10
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\n" ); document.write( "since the above series begins at k=0, I assume the series of even powers begins at k=0 also
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\n" ); document.write( "summation from k = 0 to infinity of ar^(2k), since it converges we can write
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\n" ); document.write( "2) a/(1-r^2) = 6
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\n" ); document.write( "solve equation 1 for a
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\n" ); document.write( "a = 10(1-r)
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\n" ); document.write( "substitute for a in equation 2
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\n" ); document.write( "10(1-r)/(1-r^2) = 6
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\n" ); document.write( "(1-r)/(1-r)(1+r) = 6/10
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\n" ); document.write( "1/(1+r) = 3/5
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\n" ); document.write( "cross multiply the fractions
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\n" ); document.write( "5 = 3 +3r
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\n" ); document.write( "r = 2/3
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\n" ); document.write( "a = 10(1-(2/3)) = 10/3
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\n" ); document.write( "(10/3) + (2/3) = 12/3 = 4
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