document.write( "Question 1163462: without computing each sum, find which is greater,O or E. O=5+7+9+...+99 and E=4+6+8+10+...+100? \n" ); document.write( "
Algebra.Com's Answer #787556 by Boreal(15235)\"\" \"About 
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There are 100 potential integers, 50 even and 50 odd.
\n" ); document.write( "Two of the odd are not counted (1 and 3)
\n" ); document.write( "One of the even is not counted (2).
\n" ); document.write( "The way to line them up is:
\n" ); document.write( "4+6+8+10+...+100. there are 49 even numbers in the series
\n" ); document.write( "---5+7+9+...+99. There are 48 odd numbers in the series
\n" ); document.write( "The even is greater with a larger number for the last 48 in the series and a leading number of 4 as well.\r
\n" ); document.write( "\n" ); document.write( "There are 48 pairs where E is 1 greater and a 4 that is not paired, so 52 greater.
\n" ); document.write( "if you want the sum (not the question)
\n" ); document.write( "(n/2)*(2a+(n-1)d)
\n" ); document.write( "(49/2)*(8+48*2)=2548 for the even\r
\n" ); document.write( "\n" ); document.write( "(48/2)*(10+47*2)=2496 for the odd
\n" ); document.write( "They sum to 5044
\n" ); document.write( "add the missing numbers 1,2,3 and the sum is 5050, the sum of the first hundred integers
\n" ); document.write( "n(n+1)/2=100*101/2=5050\r
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