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!