document.write( "Question 957196: if we list all the natural numbers below 10 that are multiples of 3 or 5, we get
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Algebra.Com's Answer #584834 by Edwin McCravy(20056)\"\" \"About 
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if we list all the natural numbers below 10 that are
\n" ); document.write( "multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of
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\n" ); document.write( "of 3 or 5 below 2812.
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document.write( "2812 divided by 3 is 937.333333...\r\n" );
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document.write( "So there are 937 multiples of 3 less than 2812,\r\n" );
document.write( "the last of which is (937)(3)=2811\r\n" );
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document.write( "Their sum is\r\n" );
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document.write( "3+6+9+12+15+18+21+24+27+30+...+2805+2808+2811\r\n" );
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document.write( "Therefore we use the sum formula\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\", with n=937, a1=3, d=3.\r\n" );
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document.write( "\"S%5B937%5D=expr%28937%2F2%29%283%2B2811%29=expr%28937%2F2%29%282814%29=1318359\"\r\n" );
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document.write( "----------------------------\r\n" );
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document.write( "2812 divided by 5 is 562.4\r\n" );
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document.write( "So there are 562 multiples of 5 less than 2812,\r\n" );
document.write( "the last of which is (562)(5)=2810\r\n" );
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document.write( "Their sum is\r\n" );
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document.write( "5+10+15+20+25+30+35+40+45+...+2805+2810\r\n" );
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document.write( "Therefore we use the sum formula\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\", with n=562, a1=5, d=5.\r\n" );
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document.write( "\"S%5B562%5D=expr%28562%2F2%29%285%2B2810%29=%28281%29%282815%29=791015\"\r\n" );
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document.write( "------\r\n" );
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document.write( "If we add those two sums together we get\r\n" );
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document.write( "1318359+791015 = 2109374\r\n" );
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document.write( "However that's too much because it adds the integers which are\r\n" );
document.write( "multiples of both 3 and 5 twice.  Those are the multiples of 15.\r\n" );
document.write( "So we must find the sum of the multiples of 15 below 2812 and \r\n" );
document.write( "subtract that from the 2109374:\r\n" );
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document.write( "2812 divided by 15 is 187.46666...\r\n" );
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document.write( "So there are 187 multiples of 15 less than 2812,\r\n" );
document.write( "the last of which is (187)(15)=2805\r\n" );
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document.write( "Their sum is\r\n" );
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document.write( "15+30+45+60+75+90+105+120+135+...2790+2805\r\n" );
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document.write( "Therefore we use the sum formula\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\", with n=187, a1=15, a187=2805 \r\n" );
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document.write( "\"S%5B187%5D=expr%28187%2F2%29%2815%2B2805%29=expr%28187%2F2%29%282820%29=263670\"\r\n" );
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document.write( "So subtracting 263670 from 2109374, the final answer is:\r\n" );
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document.write( "2109374-263670 = 1845704\r\n" );
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document.write( "Edwin
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