document.write( "Question 1013535: Show that the sum of nth term of the series log3+log6+log12+.... Is nlog3+n(n-1)log2/2 \n" ); document.write( "
Algebra.Com's Answer #630072 by Edwin McCravy(20055)\"\" \"About 
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document.write( "\"log%28%283%29%29%2Blog%28%286%29%29%2Blog%28%2812%29%29%2B%22%22%2A%22%22%2A%22%22%2A%22%22\"\r\n" );
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document.write( "We first get the nth term of the sequence\r\n" );
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document.write( "3,6,12,...\r\n" );
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document.write( "That's a geometric series with a1 = 3, r = 2\r\n" );
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document.write( "The nth term of that sequence is a∙rn-1 or 3∙2n-1\r\n" );
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document.write( "So the log series is\r\n" );
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document.write( "We write each number in parentheses as a product of 3 and some\r\n" );
document.write( "other number:\r\n" );
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document.write( "Now we use the principle that the log of a product equals the sum\r\n" );
document.write( "of the logs of the factors:\r\n" );
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document.write( "Since there are n terms, there and n log(3)'s added so the above \r\n" );
document.write( "sequence is:\r\n" );
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document.write( "We write each number, 1,2,4,...2n-1 in the parentheses are powers of 2.\r\n" );
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document.write( "Use the principle of logs that says that the log of an exponential is the\r\n" );
document.write( "exponent times the log of the base:\r\n" );
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document.write( "We factor out log(2)\r\n" );
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document.write( "The series in parentheses is an arithmetic series with a1 = 0,\r\n" );
document.write( "common difference 1 and number of terms n.  We use the sum formula for\r\n" );
document.write( "the series in parentheses:\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%28a%5B1%5D%5E%22%22%2Ba%5Bn%5D%29\"\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%280%2B%28n-1%29%5E%22%22%29\"\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%28n-1%29\"\r\n" );
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document.write( "Substituting for the series in parentheses:\r\n" );
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document.write( "\"n%2Alog%28%283%29%29%2Blog%28%282%29%29%2A%28+expr%28n%2F2%29%28n-1%29+%29\"\r\n" );
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document.write( "\"n%2Alog%28%283%29%29%2Bn%28n-1%29log%28%282%29%29%2F2\"\r\n" );
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document.write( "Edwin
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