https://file.aiquickdraw.com/mathbot/file/1726929320986ji6kuwkn.jpg

The image you provided shows a double summation notation. Specifically, it seems to represent the following mathematical expression:

\[
\sum_{j=2}^{4} \sum_{i=1}^{5} f(i,j)
\]

This notation indicates two nested sums, where:

- The outer sum runs with index \( j \) from 2 to 4.
- The inner sum runs with index \( i \) from 1 to 5.

Here's a step-by-step explanation of how to evaluate this double summation:

1. **Evaluate the Inner Sum for each \( j \)**: First, for each fixed value of \( j \), sum the function \( f(i, j) \) as \( i \) runs from 1 to 5.
   
   That is, compute:
   \[
   \sum_{i=1}^{5} f(i, j)
   \]
   for \( j = 2, 3, 4 \).

2. **Evaluate the Outer Sum**: After calculating the inner sums for each \( j \), sum the results over \( j = 2, 3, 4 \).

   That is:
   \[
   \sum_{j=2}^{4} \left( \sum_{i=1}^{5} f(i, j) \right)
   \]

### Next Steps:
To continue with the solution, we need to know the explicit form of the function \( f(i,j) \) or any additional context or values for \( f(i,j) \).

Let me know if you have this information or if you'd like me to walk through an example where \( f(i,j) \) is a simple function (like \( f(i,j) = i + j \)).

---

Do you want more details or have any questions so far?

Here are 5 related questions to consider:
1. What is the function \( f(i,j) \) in your problem?
2. How would the solution change if \( f(i,j) \) is a constant function?
3. Can you extend the summation to different limits for \( i \) and \( j \)?
4. How does the order of summation affect the final result in double sums?
5. What happens if the sum is dependent on a non-linear function, such as \( f(i,j) = i^2 + j \)?

**Tip:** Breaking complex summations into simpler parts (like calculating inner sums first) helps avoid confusion and errors!

What does this double summation notation represent and how is it evaluated?

Explore the double summation notation \sum_{j=2}^{4} \sum_{i=1}^{5} f(i,j) with a step-by-step guide on its evaluation. Learn about iterated sums and how to compute them effectively. Suitable for college-level mathematics students.

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