https://file.aiquickdraw.com/mathbot/file/17273048271475gdc8wts.jpg

It seems that the text extraction from the image wasn't successful. Based on the image, I can manually interpret the expression.

The expression you provided appears to be:

\[
\prod_{n=1}^{j} \left( \sum_{k=1}^{j} n \cdot k \right)
\]

This represents:

- The product (denoted by the capital pi symbol \( \prod \)) from \( n = 1 \) to \( j \),
- Inside the product, there is a summation (denoted by the capital sigma symbol \( \sum \)) from \( k = 1 \) to \( j \),
- The term being summed is \( n \cdot k \).

Would you like further details or explanation about how to evaluate or interpret this expression?

Here are some questions to extend your understanding:
1. How do you calculate products of sums in this type of expression?
2. What role does the index \( n \) play in both the product and the sum?
3. How would the expression simplify for a specific value of \( j \), say \( j = 2 \)?
4. What is the difference between a product notation and a sum notation in mathematics?
5. How does this expression change if you swap the roles of \( n \) and \( k \)?

**Tip**: In product notation, multiplying terms means all intermediate results get multiplied together, not just summed up!

Understand the product and summation notation through the expression \( \prod_{n=1}^{j} \left( \sum_{k=1}^{j} n \cdot k \right) \). This problem demonstrates how to calculate products of sums, focusing on multiplication and summation rules. Suitable for Grades 10-12.

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