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Math Help - Sum of Positive Integers

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    Member Rimas's Avatar
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    Sum of Positive Integers

    Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2
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    Quote Originally Posted by Rimas View Post
    Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2
    3,6,9,12,15,....,999
    How many? Answer (333)

    Now list all those divisible by 2:
    6,12,18,....,996
    How many? Answer (83)

    Subtract them to get answer.
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  3. #3
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    Rimas and I are friends, and you seem to have read the problem wrong like I did intially. The problem asks for the sum of the integers, not how many integers.

    I already determined that the sum of all integers divisible by 3 and 2 is 82,170 if that helps any.
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  4. #4
    Senior Member DivideBy0's Avatar
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    To solve this problem, you have to know this formula: n/2 * (a + L), where a is the first number in the series, L is the last number in the series, and n is the number of numbers in the series. It gives the sum of the series.

    So... you have to sum every multiple of 3 first. As there are 333 of them, the first is 3, and the last is 999, sub that in to find the sum:

    333/2 * (3 + 999) = 166833

    Next, subtract all the number divisible by both 2 and 3 (that is, numbers divisible by 2*3 = numbers divisible by 6). As there are 166 of them, the first is 6 and the last is 996, sub that in to find the sum:

    166/2 * (6 + 996) = 83166

    Now, simply subtract 83166 from 166833:

    166833 - 83166 = 83667

    If you have any questions regarding the formula or anything else feel free to ask.
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  5. #5
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    Hello, Rimas!

    Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2
    The numbers divisible by 3 are: .3, 6, 9, 12, 15, 18, ... , 999

    We see that every other number is divisible by 2, so we omit those.

    And we have: .3, 9, 15, 21, ..., 999, .an arithmetic sequence
    . . with first term a = 3, common difference d = 6, and n = 167 terms.

    The sum of the series is: .(167) [2(3) + 166(6)] .= .83,667

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