document.write( "Question 1113759: The sum of the series 1/√3+1+3/√3+........... To 18 terms is ??
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Algebra.Com's Answer #728853 by KMST(5328) $\"\"$ $\"About$

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It is a geometric series, with first term $\"b=1%2Fsqrt%283%29\"$ and common ratio $\"r=sqrt%283%29\"$ .
\n" ); document.write( "The sum of the first $\"n\"$ terms of a geometric series with first term $\"b\"$ and common ratio $\"r\"$ is
\n" ); document.write( " $\"b%28%28r%5En-1%29%2F%28r-1%29%29\"$ .
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\n" ); document.write( "In this case, the sum of the first $\"n=18\"$ terms would be
\n" ); document.write( " $\"%281%2Fsqrt%283%29%29%28%28sqrt%283%29%5E18-1%29%2F%28sqrt%283%29-1%29%29\"$ $\"%22=%22\"$ $\"%281%2Fsqrt%283%29%29%28%28%283%5E%221+%2F+2%22%29%5E18-1%29%2F%28sqrt%283%29-1%29%29\"$ $\"%22=%22\"$

$\"%22=%22\"$

$\"%22=%22\"$ $\"19682%283%2Bsqrt%283%29%29%2F%283%283-1%29%29\"$ $\"%22=%22\"$ $\"19682%283%2Bsqrt%283%29%29%2F6\"$ $\"%22=%22\"$ $\"highlight%289841%283%2Bsqrt%283%29%29%2F3%29\"$ $\"%22=%22\"$ $\"approximately15522.7\"$
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\n" ); document.write( "ANOTHER WAY:
\n" ); document.write( "The 9 even numbered terms are
\n" ); document.write( " $\"matrix%281%2C7%2C%0D%0A1%2C%22%2C%22%2C3%2C%22%2C%22%2C9%2C%22%2C...%2C%22%2C3%5E8=6561%29\"$ and add up to $\"1%283%5E9-1%29%2F%283-1%29=%2819683-1%29%2F2=9841\"$ .
\n" ); document.write( "The 9 odd numbered terms must add up to $\"9841%2Fsqrt%283%29\"$ .
\n" ); document.write( "Adding up both of those sums, we get
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