document.write( "Question 1209367: Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5 or 8. \n" ); document.write( "

Algebra.Com's Answer #848682 by math_helper(2461) $\"\"$ $\"About$

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document.write( "I'm going to do more work than the problem requires, to make sure I'm doing
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document.write( "it correctly, and hopefully this method helps you gain some intuition.\r
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document.write( "Sum of all positive integers less than 1000 ending in 0:
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document.write( "Sum(0+10n; n=0,...,99) = 0*sum(0, n=0,...,99) + 10*sum(0...99) = 10*(99*100/2) 
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document.write( "  = 0 + 49500 = 49500\r
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document.write( "Sum of all positive integers less than 1000 ending in 1:
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document.write( "Sum(1+10n; n=0,...,99) = 1*sum(1, n=0,...,99) + sum(10n, n=0,...,99)
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document.write( " = 100 + 49500 = 49600\r
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document.write( "Repeating the above two calculations and noting we just add 100 for each
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document.write( "higher digit:\r
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document.write( "Sum of all positive integers less than 1000 ending in 0:   49500
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document.write( "Sum of all positive integers less than 1000 ending in 1:   49600
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document.write( "Sum of all positive integers less than 1000 ending in 2:   49700 
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document.write( "Sum of all positive integers less than 1000 ending in 3:   49800 (#)
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document.write( "Sum of all positive integers less than 1000 ending in 4:   49900 (#)
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document.write( "Sum of all positive integers less than 1000 ending in 5:   50000 (#)
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document.write( "Sum of all positive integers less than 1000 ending in 6:   50100
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document.write( "Sum of all positive integers less than 1000 ending in 7:   50200
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document.write( "Sum of all positive integers less than 1000 ending in 8:   50300 (#)
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document.write( "Sum of all positive integers less than 1000 ending in 9:   50400
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document.write( "                                                  total:  499500\r
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document.write( "Sanity check the above total, which should be the same as ALL numbers 0...999:
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document.write( "Sum(n; n=0,...,999) = 999*1000/2 = 499500   \r
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document.write( "Sum the rows with (#), you should get 200000
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