document.write( "Question 1120335: what is the harmonic sequence of 3/2, 1/2, 3/10, 3/14... n= 9? \n" ); document.write( "

Algebra.Com's Answer #736024 by Edwin McCravy(20056) $\"\"$ $\"About$

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what is the harmonic sequence of 3/2, 1/2, 3/10, 3/14, ... n=9?
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document.write( "A harmonic sequence is a sequence of the reciprocals of the terms of an\r\n" );
document.write( "arithmetic sequence.  Therefore we look at the arithmetic sequence\r\n" );
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document.write( "2/3, 2/1, 10/3, 14/3,...\r\n" );
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document.write( "2/1-2/3 = 6/3-2/3 = 4/3\r\n" );
document.write( "10/3-2/1 = 10/3-6/3 = 4/3\r\n" );
document.write( "14/3-10/3 = 4/3\r\n" );
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document.write( "So we add common difference 4/3 successively until we have\r\n" );
document.write( "9 terms:\r\n" );
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document.write( "14/3+4/3 = 18/3 = 6/1\r\n" );
document.write( " 6/1+4/3 = 18/3+4/3 = 22/3\r\n" );
document.write( "22/3+4/3 = 26/3\r\n" );
document.write( "26/3+4/3 = 30/3 = 10/1\r\n" );
document.write( "10/1+4/3 = 30/3+4/3 = 34/3\r\n" );
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document.write( "2/3, 2/1, 10/3, 14/3, 6, 22/3, 26/3, 10/1, 34/3\r\n" );
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document.write( "That's the arithmetic sequence of reciprocals of the harmonic\r\n" );
document.write( "sequence.  So the harmonic sequence is the sequence of\r\n" );
document.write( "reciprocals of the arithmetic sequence:\r\n" );
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document.write( "3/2, 1/2, 3/10, 3/14, 1/6, 3/22, 3/26, 1/10, 3/34\r\n" );
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document.write( "Edwin

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