document.write( "Question 1035578: Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, leaving out the multiples of 3. \n" ); document.write( "

Algebra.Com's Answer #650230 by ikleyn(52793) $\"\"$ $\"About$

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document.write( "Calculate the sum of all integers from 1 to 300 inclusively.\r\n" );
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document.write( "It is  = 45150.     (1) \r\n" );
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document.write( "(use the known formula for the sum of arithmetic progression.\r\n" );
document.write( "See the lesson Arithmetic progressions in this site).\r\n" );
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document.write( "Next, calculate the sum of the integers from 0 to 300 that are multiples of 3.\r\n" );
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document.write( "It is 3*(1 + 2 + 3 + . . . + 100) =  = 3*5050 = 15150.   (2)\r\n" );
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document.write( "Again, use the formula for the sum of AP.\r\n" );
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document.write( "As a final step, distract (2) from (1): 45150 - 15150 = 30000.\r\n" );
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document.write( "Answer.  30000.\r\n" );
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