document.write( "Question 1041235: Find the sum of the first n positive even integer\r
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Algebra.Com's Answer #656209 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "2 + 4 + 6 + . . . 2n = 2*(1 + 2 + 3 + . . . + n).     (1)\r\n" );
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document.write( "The sum (1 + 2 + 3 + . . . +n) is very well known. \r\n" );
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document.write( "It is the sum of the first \"n\" positive integers.\r\n" );
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document.write( "It is also the sum of \"n\" terms of an arithmetic progression with the first term 1 and the common difference 1.\r\n" );
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document.write( "This sum is equal to .\r\n" );
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document.write( "See, for example, the lessons \r\n" );
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document.write( "    - Arithmetic progressions\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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document.write( "So, your sum (1) is equal to n*(n+1).\r\n" );
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document.write( "Let us check the first sums , , :\r\n" );
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document.write( "n=1:   = 2.                     n*(n+1) = 1*2 = 2.\r\n" );
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document.write( "n=2:   = 2 + 4 = 6.             n*(n+1) = 2*3 = 6.\r\n" );
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document.write( "n=3:   = 2 + 4 + 6 = 12.        n*(n+1) = 3*4 = 12.\r\n" );
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