document.write( "Question 1037098: 1 - 4/5 - 3/5 - 8/17 - 5/13 - ...????
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Algebra.Com's Answer #651915 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "What do you want to do with it?\r\n" );
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document.write( "I'll do what I can:\r\n" );
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document.write( "SUM = 1 - 4/5 - 3/5 - 8/17 - 5/13 - ...????\r\n" );
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document.write( "SUM = 2/2 - 4/5 - 6/10 - 8/17 - 10/26 - ...????\r\n" );
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document.write( "The sequence of absolute value of numerators is 2,4,6,8,10\r\n" );
document.write( "The sequence of absolute value of denominators is 2,5,10,17,26\r\n" );
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document.write( "2,4,6,8,10 has general term 2n\r\n" );
document.write( "1,5,10,17,26 has general term n2+1\r\n" );
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document.write( "The general term would be \"-2n%2F%28n%5E2%2B1%29\" except for the first\r\n" );
document.write( "term being positive instead of negative, so we write the first term as\r\n" );
document.write( "\"2-2%2F2\"\r\n" );
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document.write( "SUM = 2 - 2/2 - 4/5 - 6/10 - 8/17 - 10/26 - ...????\r\n" );
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document.write( "So it could be written this way:\r\n" );
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document.write( "SUM = \"2+-+sum%28%282k%2F%28k%5E2%2B1%29%29%2Ck=1%2Cn%29\"\r\n" );
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document.write( "The next term after -10/26 (or -5/13) would be \"-2%286%29%2F%286%5E2%2B1%29=-12%2F%2836%2B1%29=-12%2F37\"\r\n" );
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document.write( "It can't be summed to infinity because it diverges when compared \r\n" );
document.write( "to the harmonic p-series S(1/n).\r\n" );
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document.write( "Edwin
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