document.write( "Question 1147619: The sum of 99 consecutive odd, positive integers is the greatest perfect cube less than 999 999. Find the sum of the least and the greatest of the integers. \n" ); document.write( "

Algebra.Com's Answer #768961 by ikleyn(52858) $\"\"$ $\"About$

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document.write( "(1)  Notice that the sum of 99 consecutive odd integers is 99 times the average of the first and the last numbers in this sequence.\r\n" );
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document.write( "(2)  In other words,  the sum of 99 consecutive odd integers is 99 times half the sum of the first and the last numbers in this sequence.\r\n" );
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document.write( "(3)   = 99.99997... (approximately)\r\n" );
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document.write( "     It means that the greatest perfect cube less than 999999 is .\r\n" );
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document.write( "(4)  Thus the condition says\r\n" );
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document.write( "          = .\r\n" );
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document.write( "(5)  Hence,   +  =  = 19602.\r\n" );
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document.write( "     It is the ANSWER to the problem's question.\r\n" );
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