document.write( "Question 1035847: When the sun if the first 31 positive even integers is added to the first 32 positive off integers the result is N find N \n" ); document.write( "

Algebra.Com's Answer #650461 by ikleyn(52896) $\"\"$ $\"About$

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\n" ); document.write( "When the sun if the first 31 positive even integers is added to the first 32 positive $\"highlight%28cross%28off%29%29\"$ odd integers the result is N. Find N.
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document.write( "The sum of the first 31 positive even integers is the sum \r\n" );
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document.write( "2 + 4 + 6 + . . . + 62.    (1)\r\n" );
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document.write( "The sum of the first 32 positive odd integers is the sum \r\n" );
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document.write( "1 + 3 + 5 + . . . + 63.    (2)\r\n" );
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document.write( "When these two sums, (1) and (2) are added, the sum is\r\n" );
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document.write( "1 + 2 + 3 + 4 + 5 + 6 + . . . + 63.   (3)\r\n" );
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document.write( "It is the sum of the first 63 positive integers.\r\n" );
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document.write( "It is equal to  = 63*32 = 2016.\r\n" );
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document.write( "You can use the formula for the sum of an arithmetic progression (see the lesson Arithmetic progressions in this site) \r\n" );
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document.write( "or use the fact that the sum of the first \"n\" positive integer numbers is    \r\n" );
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document.write( "See the same lesson or/and the following two lessons\r\n" );
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document.write( "    - The proofs of the formulas for arithmetic progressions \r\n" );
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document.write( "    - Problems on arithmetic progressions \r\n" );
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document.write( "in this site.\r\n" );
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