document.write( "Question 1163476: without computing each sum find which is greater o or e and by how much o = 5+7+9+11+..+105. E = 4+6+8+10+...+104 \n" ); document.write( "

Algebra.Com's Answer #787573 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "Without computing, it is clear that the number of addends is the same in both sums.\r\n" );
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document.write( "From the other side, each addend in the first sum is 1 unit greater than the corresponding addend in the second sum.\r\n" );
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document.write( "It leads us to the conclusion that the O-value is greater than E-value.\r\n" );
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document.write( "Next, O-value is greater than E-value exactly by the number of addends in each sum.\r\n" );
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document.write( "The number of intervals of the length 2 between  4 and 104 inclusive is   =  = 50.\r\n" );
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document.write( "Hence the number of terms in each sum is 50+1 = 51.\r\n" );
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document.write( "Thus O-value is 51 units greater than E-value.\r\n" );
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