document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147618>Question 1147618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The odd integers are arranged into sets, each succeeding set continuing from the previous, and containing one more number as follows: {1},{3,5},{7,9,11},{13,15,17,19},... what is the sum of the numbers in the 22nd set? </SPAN>\n" );
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document.write( "The number of numbers in the first 21 sets is<br><BR>\n" );
document.write( "1+2+3+...+20+21 = (21*22)/2 = 231<br><BR>\n" );
document.write( "The numbers in the 22nd set are the 22 odd numbers starting with the 232nd odd number -- i.e., the 232nd through the 253rd odd numbers.<br><BR>\n" );
document.write( "So the sum of the numbers in the 22nd set is<br><BR>\n" );
document.write( "463+465+...+505 = 22*((463+505)/2) = 11*968 = 10648<br><BR>\n" );
document.write( "Another path to the answer, after finding the answer is the sum of the 232nd through the 253rd odd number....<br><BR>\n" );
document.write( "The sum of the first n odd numbers is n^2.  So the sum of the 232nd through 253rd odd number is the sum of the first 253 odd numbers minus the sum of the first 231 odd numbers:<br><BR>\n" );
document.write( "253^2-231^2 = 10648<br><BR>\n" );
document.write( " </SPAN>\n" );
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