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Find the sum of all positive integers less than 1000 ending in 3 or 7.

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5 answers

  1. First, you need to list all of the integers that match the condition. Do you know what these integers are?

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  2. Positive integers less than 1000 consist of {1 ... 999}.

    This may also be written {001 ... 999}.

    So you need to count, {003, 007, 013, ... 987, 993, 997}.

    Which is the same result as counting {00, 01, ... 98, 99} twice over. (Once for ??3, once for ??7).

    Count the number of integers from 0 and 99 inclusive. Double that.

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  3. I see it as
    (3 + 13 + 23 + + 993) + (7 + 17 + ... + 997)
    two arithmetic series,
    there are 100 terms in each series with a= 3 and d = 10 and a=7 and d=10
    using :
    sum= (n/2)(first + last)

    sum = (100/2)(3+993) + (100/2)(7+997)
    = 100,000

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  4. Thanks, guys!

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  5. No cheating >:(

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