document.write( "Question 696784: write the geometric series -9/2 + 3/2 - 1/2 + 1/6 - .......... + 1/39366 in summation notation\r
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\n" ); document.write( "\n" ); document.write( "than \r
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\n" ); document.write( "\n" ); document.write( "using the formula for the sum of an geometric series, computer the sum in the problem above \r
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Algebra.Com's Answer #429548 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
-9/2 + 3/2 - 1/2 + 1/6 - .......... + 1/39366
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document.write( "r = \"3%2F2\"÷\"-9%2F2\" = \"3%2F2\"×\"-2%2F9\" = \"%28-6%29%2F18\" = \"-1%2F3\"\r\n" );
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document.write( "an = a1rn-1 = \"%28-9%2F2%29\"×\"%28-1%2F3%29%5E%28n-1%29\" = \"%28-9%2F2%29\"×\"%28-1%2F3%29%5E%28n-1%29\"\r\n" );
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document.write( "\"%28-9%2F2%29\"×\"%28-1%2F3%29%5E%28n-1%29\" = \"1%2F39366\"\r\n" );
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document.write( "Multiply both sides by \"-2%2F9\"\r\n" );
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document.write( "\"-2%2F9\"×\"%28-9%2F2%29\"×\"%28-1%2F3%29%5E%28n-1%29\" = \"-2%2F9\"×\"1%2F39366\"\r\n" );
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document.write( "             \"%28-1%2F3%29%5E%28n-1%29\" = \"-2%2F9\"×\"1%2F39366\"\r\n" );
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document.write( "             \"%28-1%2F3%29%5E%28n-1%29\" = \"-2%2F%289%2A39366%29\"\r\n" );
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document.write( "             \"%28-1%29%5E%28n-1%29%281%2F3%29%5E%28n-1%29\" = \"-1%2F%289%2A19683%29\"\r\n" );
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document.write( "             \"%28-1%29%5E%28n-1%29%281%2F3%29%5E%28n-1%29\" = \"-1%2F177147\"\r\n" );
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document.write( "n-1 must be an odd number since the right side is negative,\r\n" );
document.write( "so (-1)n-1 = -1.   Therefore, dividing both sides\r\n" );
document.write( "by -1,\r\n" );
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document.write( "             \"%281%2F3%29%5E%28n-1%29\" = \"1%2F177147\" \r\n" );
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document.write( "             \"1%2F3%5E%28n-1%29\" = \"1%2F177147\" \r\n" );
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document.write( "taking reciprocals of both sides:\r\n" );
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document.write( "             3n-1 = 177147\r\n" );
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document.write( "Taking the natural log of both sides\r\n" );
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document.write( "           ln(3n-1) = ln(177147)\r\n" );
document.write( "           (n-1)ln(3) = ln(177147)\r\n" );
document.write( "                  n-1 = \"ln%28177147%29%2Fln%283%29\"\r\n" );
document.write( "                  n-1 = 11\r\n" );
document.write( "                    n = 12\r\n" );
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document.write( "So there are 12 terms:\r\n" );
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document.write( "Summation  = \"sum%28%28-9%2F2%29%28-1%2F3%29%5E%28n-1%29%2C1%2C12%29\"\r\n" );
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document.write( "Sn = \"%28a%5B1%5D%281-r%5En%29%29%2F%281-r%29\" = \"%28-9%2F2%29%281-%28-1%2F3%29%5E12%29%2F%281-%28-1%2F3%29%29\" = \"%28-9%2F2%29%281-%28-1%2F3%29%5E12%29%2F%281%2B1%2F3%29\" = \"%28-9%2F2%29%281-%28-1%2F3%29%5E12%29%2F%284%2F3%29\"\r\n" );
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document.write( "= \"%28-9%2F2%29%281-%28-1%2F3%29%5E12%29%2A%283%2F4%29\" = \"%28-9%2F2%29%281-1%2F3%5E12%29%2A%283%2F4%29\" = \"%28-27%2F8%29%281-1%2F3%5E12%29\" = -3.37499365   \r\n" );
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document.write( "The computer program I have is Liberty Basic of which you can download\r\n" );
document.write( "a free trial version.   Here is the Liberty Basic program I wrote\r\n" );
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document.write( "A1 = -9/2\r\n" );
document.write( "r = -1/3\r\n" );
document.write( "for n = 1 to 12\r\n" );
document.write( "An = A1*r^(n-1)\r\n" );
document.write( "sum = sum+An\r\n" );
document.write( "print \"A(\";n;\") = \";An;\", sum =\";sum\r\n" );
document.write( "next\r\n" );
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document.write( "Here is the output of that program:\r\n" );
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document.write( "A(1) = -4.5, sum =-4.5\r\n" );
document.write( "A(2) = 1.5, sum =-3\r\n" );
document.write( "A(3) = -0.5, sum =-3.5\r\n" );
document.write( "A(4) = 0.16666667, sum =-3.33333333\r\n" );
document.write( "A(5) = -0.55555556e-1, sum =-3.38888889\r\n" );
document.write( "A(6) = 0.18518519e-1, sum =-3.37037037\r\n" );
document.write( "A(7) = -0.61728395e-2, sum =-3.37654321\r\n" );
document.write( "A(8) = 0.20576132e-2, sum =-3.3744856\r\n" );
document.write( "A(9) = -0.68587106e-3, sum =-3.37517147\r\n" );
document.write( "A(10) = 0.22862369e-3, sum =-3.37494284\r\n" );
document.write( "A(11) = -0.76207895e-4, sum =-3.37501905\r\n" );
document.write( "A(12) = 0.25402632e-4, sum =-3.37499365\r\n" );
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document.write( "Edwin
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