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Math Help - (FP1) summation of finite series using standard results

  1. #1
    Member ssadi's Avatar
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    Question (FP1) summation of finite series using standard results

    Find the sum of all even numbers between 2 and 200 inclusive, excluding those which are multiples of 3.
    My answer:3467
    Book's answer:6734
    Bamboozled by the toggling of digits here, I need help to of you as to which is the right answer.
    This may be a typo by the book's typist, who knows.
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  2. #2
    Moo
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    Hello,

    Sum of all even numbers between 2 and 200 :
    2+4+ \dots + 200=2(1+2+\dots+100)=2 \sum_{n=1}^{100} n

    Among these (integers from 1 to 100), remove the ones in the form 3k

    Sum of all multiples of 3 between 1 and 100 :
    3+6+\dots+99=3(1+2+\dots+33)=3 \sum_{n=1}^{33} n

    So S=2 \left( \sum_{n=1}^{100} n-3 \sum_{n=1}^{33} n\right)

    S=2 \left(\frac{100 \times 101}{2}-3 \cdot \frac{33 \times 34}{2} \right)

    S=2 \left(50 \times 101-3 \times 33 \times 17 \right)

    S=6734
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  3. #3
    Member ssadi's Avatar
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    Thumbs up Solved

    Quote Originally Posted by Moo View Post
    Hello,

    Sum of all even numbers between 2 and 200 :
    2+4+ \dots + 200=2(1+2+\dots+100)=2 \sum_{n=1}^{100} n

    Among these (integers from 1 to 100), remove the ones in the form 3k

    Sum of all multiples of 3 between 1 and 100 :
    3+6+\dots+99=3(1+2+\dots+33)=3 \sum_{n=1}^{33} n

    So S=2 \left( \sum_{n=1}^{100} n-3 \sum_{n=1}^{33} n\right)
    I misunderstood the question, thanks for helping me out.
    S=2 \left(\frac{100 \times 101}{2}-3 \cdot \frac{33 \times 34}{2} \right)

    S=2 \left(50 \times 101-3 \times 33 \times 17 \right)

    S=6734
    I misunderstood the question, thanks for helping me out
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