Calculating Double Sum: (n=3)(i=0)∑(n=2)(j=0)∑(3i+2j)

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In summary, the formula for calculating double sum involves two sums, one for the outer variable (i) and one for the inner variable (j). The variables n, i, and j represent the upper limit, the outer sum, and the inner sum respectively. To solve a double sum problem, the upper limit and variables must be identified, and the expression must be evaluated and added together. The purpose of calculating double sum is to analyze data and make predictions based on multiple factors. The order of the variables can be changed as long as the upper limit remains the same, but the expression must remain the same.
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Homework Statement



Compute the following double sum

(n=3)(i=0)[tex]\sum[/tex](n=2)(j=0)[tex]\sum[/tex](3i+2j)

Homework Equations



sums

The Attempt at a Solution



my answer follows expanding the first sum, then just doing the last one

i get

(n=3)(i=0)[tex]\sum[tex](6+9i) = 78

thanks!
 
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[tex]\sum_{i=0}^{n=3} \sum_{j=0}^{n=2}(3i+2j)=\sum_{i=0}^{n=3}(6+9i)=78[/tex]

Looks good to me.
 

What is the formula for calculating double sum?

The formula for calculating double sum is given as (n=3)(i=0)∑(n=2)(j=0)∑(3i+2j). This means that the outer sum is for i=0 to n=3, and the inner sum is for j=0 to n=2. The sum of (3i+2j) is calculated for each value of i and j, and then added together.

What do the variables n, i, and j represent in the double sum formula?

In the double sum formula, n represents the upper limit of the summation, i represents the variable for the outer sum, and j represents the variable for the inner sum. These variables determine the range of values to be summed and the expression to be evaluated for each value.

How do you solve a double sum problem?

To solve a double sum problem, follow these steps:

  1. Determine the upper limit for each sum (n).
  2. Identify the variables for the outer and inner sums (i and j).
  3. Write the expression to be evaluated for each value of i and j.
  4. Calculate the value of the expression for each combination of i and j.
  5. Add all the values together to get the final result.

What is the purpose of calculating double sum?

The purpose of calculating double sum is to find the sum of a series of numbers that are dependent on two variables. This is often used in mathematical and scientific fields to analyze data and make predictions based on multiple factors.

Can the order of the variables in a double sum formula be changed?

Yes, the order of the variables in a double sum formula can be changed as long as the upper limit (n) remains the same. This means that the outer and inner sums can be switched without affecting the final result. However, the expression to be evaluated for each value of i and j must remain the same.

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