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Math Help - Nested sums (sigma notation)

  1. #1
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    Exclamation Nested sums (sigma notation)

    I am having difficulty with converting nested sigma notations into closed forms.

    sum [from i=3 to n] (i * sum [from j=i+1 to n] (3) )

    I apologize for the notation but I hope I portrayed the question.

    The inner one I thought that it would be i(n- (i+1) +1)3 = 3i(n-i) {which I thought is the closed form for a constant} then substitute into the outer one.

    Any help or explanation muchly appreciated.

    Ray
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  2. #2
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    Quote Originally Posted by R.Laramee View Post
    I am having difficulty with converting nested sigma notations into closed forms.

    sum [from i=3 to n] (i * sum [from j=i+1 to n] (3) )

    I apologize for the notation but I hope I portrayed the question.

    The inner one I thought that it would be i(n- (i+1) +1)3 = 3i(n-i) {which I thought is the closed form for a constant} then substitute into the outer one.

    Any help or explanation muchly appreciated.

    Ray
    3i(n - i) = 3ni - 3i^2

    \sum_{i=3}^n (3ni - 3i^2) = 3n \sum_{i=3}^n i - 3 \sum_{i=3}^n i^2 ......
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  3. #3
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    The inner summation is multiplied by i. Do I multiply it through before I calculate the outer? So therefore 3n sum(i^2) - 3 sum(i^3)? Then used the closed forms for ^2 and ^3 respectively?

    Thanks for what you have given so far and once again I apologize for notation.
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