Algebra.Com's Answer #792916 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The sum of 128 consecutive odd, positive integers is the greatest power of two less than 200,000.
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document.write( "The sum of the least and the greatest of these integers is 2^N. What is the value of N?
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document.write( " = 17.61 (approximately, with two decimals).\r\n" );
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document.write( "Therefore, the greatest power of 2 less than 200,000 is  = 131072.\r\n" );
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document.write( "So, the sum of 128 consecutive odd positive integers is 131072.\r\n" );
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document.write( "These consecutive integer numbers form an arithmetic progression;\r\n" );
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document.write( "therefore, their sum is the product of the number of terms (128) by half the sum of the least and the greatest of these two numbers.\r\n" );
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document.write( "In other words, =  .\r\n" );
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document.write( "It is equivalent to\r\n" );
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document.write( " =  , or\r\n" );
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document.write( " =  , or\r\n" );
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document.write( " =  .\r\n" );
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document.write( "It implies 17 = N + 6, or N = 17 - 6 = 11.\r\n" );
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document.write( "ANSWER. N = 11.\r\n" );
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document.write( "Solved.\r
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