# Math Help - Nested sums (sigma notation)

1. ## 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

2. Originally Posted by R.Laramee
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
$3i(n - i) = 3ni - 3i^2$

$\sum_{i=3}^n (3ni - 3i^2) = 3n \sum_{i=3}^n i - 3 \sum_{i=3}^n i^2$ ......

3. 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.