document.write( "Question 1131912: Write geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366 in summation notation. Using the formula for the sum of an geometric series, compute the sum in the problem above. \n" ); document.write( "
Algebra.Com's Answer #748651 by ikleyn(52776)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by  @MathLover1  seems to be almost infinitely long;
\n" ); document.write( "            but it can be implemented much shorter,  without making unnecessary calculations.
\n" ); document.write( "            See my solution below.\r
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document.write( "The common ratio is  q = \"3%2F2\" : \"-9%2F2\" = \"%28%283%2F2%29%29%2F%28%28-9%2F2%29%29\" = \"3%2F%28-9%29\" = \"-1%2F3\".\r\n" );
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document.write( "The formula for the sum of \"n\" first term of an geometry progression is\r\n" );
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document.write( "    S = \"%28a%5B1%5D%2Aq%5En-a%5B1%5D%29%2F%28q-1%29\".\r\n" );
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document.write( "We have  \"a%5B1%5D\" = \"-9%2F2\"  and  \"a%5B1%5D%2Aq%5E%28n-1%29\" = \"1%2F39366\"  (the n-th term).\r\n" );
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document.write( "Therefore,  \r\n" );
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document.write( "    S = \"%28a%5B1%5D%2Aq%5E%28n-1%29%2Aq+-+a%5B1%5D%29%2F%28q-1%29\" = \"%28%281%2F39366%29%2A%28-1%2F3%29-%28-9%2F2%29%29%2F%28%28-1%2F3%29-1%29\" = \"%281%2F%283%2A39366%29+-+9%2F2%29%2F%28%284%2F3%29%29\" = \"%28%282+-+9%2A3%2A39366%29%29%2F%28%282%2A3%2A39366%29%29%2F%28%284%2F3%29%29\" = \"%282-9%2A3%2A39366%29%2F%288%2A39366%29\" = \"-1062880%2F314928\" = \"-66430%2F19683\" = \"-3\"\"7381%2F19683\".\r\n" );
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