Algebra.Com's Answer #689047 by ikleyn(52798)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9.
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document.write( "The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 4133.
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document.write( "1. Take the sum  of all integer numbers multiple of 3 from 1 to 4133.\r\n" );
document.write( " It is the sum of an AP with the first term 3, the common difference 3 and the last term of 4131. \r\n" );
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document.write( " The number of terms is n =  = 1377.\r\n" );
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document.write( "2. Take the sum  of all integer numbers multiple of 5 from 1 to 4133.\r\n" );
document.write( " It is the sum of an AP with the first term 5, the common difference 5 and the last term of 4130. \r\n" );
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document.write( " The number of terms is n =  = 826.\r\n" );
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document.write( "3. Calculate  .\r\n" );
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document.write( " Still, it is NOT your answer.\r\n" );
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document.write( "4. To get the answer, distract from the sum  of all integer numbers multiple of 15 from 1 to 4133. \r\n" );
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document.write( " ( Since you counted these numbers TWICE in the sum (!) )\r\n" );
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document.write( " The sum is the sum of an AP with the first term 15, the common difference of 15 and the last term 4125.\r\n" );
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document.write( " The number of terms is n =  = 275.\r\n" );
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document.write( "5. Again, your answer will be  .\r\n" );
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document.write( " Do all these calculations on your own.\r\n" );
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document.write( " You have clear instructions. The rest is simple arithmetic.\r\n" );
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document.write( "On calculating the sum of an arithmetic progression see the lesons\r
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document.write( " - Arithmetic progressions\r
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document.write( " - The proofs of the formulas for arithmetic progressions \r
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document.write( " - Problems on arithmetic progressions \r
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document.write( "in this site.\r
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
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document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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