document.write( "Question 744746: Find the sum of the odd integers between
\n" ); document.write( "-39 and 91 including them, that is,
\n" ); document.write( "-39+(-37)+(-35)+....+49+91 \n" ); document.write( "
Algebra.Com's Answer #453564 by fcabanski(1391)\"\" \"About 
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The sum of -39 ...+39 = 0. -39 + 39 - 0. -37 + 37 = 0 etc.


\n" ); document.write( "This is the sum of odd integers from 41 to 91.


\n" ); document.write( "The sum of n odd integers is \"n%5E2\"


\n" ); document.write( "The number, n, of odd positive integers from 0 up to a certain odd integer is ((that integer - 1)/2) + 1. For example, the number (n) of odd integers from 0 to 9 is ((9-1)/2) + 1 = 5. The odd integers from 0 to 9 are 1, 3, 5, 7, 9 - there are five.


\n" ); document.write( "The number of odd integers from 0 to 91 is 91-1 = 90/2=45 + 1 = 46. \"46%5E2+=+2116\".


\n" ); document.write( "Subtract the sum of odd integers from 0 to 39 (because those summed to 0 when added to -1, -3...-39). There are (39-1)/2 = 19 + 1 = 20 odd integers from 0 to 37. \"20%5E2+=+400\"


\n" ); document.write( "The sum of all odd numbers from 0 to 91 - the sum of all odd numbers from 0 to 39 is the sum of odd numbers from 41 to 91. It is 2116-400 = 1716.\r
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