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Math Help - sigma notation

  1. #1
    Junior Member
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    sigma notation

    how to write in correct way:

    to calculate the sum of odd numbers between 1 and n;

    to calculate the sum of even numbers between 2 and n;

    my suggestion about odd numbers:

    n
    E (i+2) --> do you agree?
    i=2
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  2. #2
    Junior Member CuriosityCabinet's Avatar
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    I would say, for even numbers:

    \sum_{i=0}^{n}(2i+2)

    and for odd:

    \sum_{i=0}^{n}(2i+1)
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  3. #3
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    Quote Originally Posted by problady View Post
    how to write in correct way:

    to calculate the sum of odd numbers between 1 and n;

    to calculate the sum of even numbers between 2 and n;

    my suggestion about odd numbers:

    n
    E (i+2) --> do you agree?
    i=2
    \displaystyle\sum_{i=2}^n(i+2)=4+5+6+.....+(n-1)+n+(n+1)+(n+2)


    Instead...for n odd

    \displaystyle\sum_{i=1}^{\frac{n+1}{2}}(2i-1)=1+3+5+...+n

    or

    \displaystyle\sum_{i=0}^{\frac{n-1}{2}}(2i+1)=1+3+5+...+n


    for n even, sum of the odd numbers is...

    \displaystyle\sum_{i=1}^{\frac{n}{2}}(2i-1)=1+3+5+...+(n-1)


    or

    \displaystyle\sum_{i=0}^{\frac{n-2}{2}}(2i+1)=1+3+5+...+(n-1)

    That's if "between" is meant to include i=1 and i=n, rather than exclude them
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