To express the given sum in sigma notation, let's analyze the pattern in the terms provided:

Each term is of the form: $\left(3 - \frac{j}{7}\right)^2$ where $j$ is an integer that increments by 1, starting from $j = 1$ up to $j = 7$.

Therefore, the sum can be represented as: $\sum_{j=1}^{7} \left(3 - \frac{j}{7}\right)^2$

So, the complete answer in sigma notation is: $\sum_{j=1}^{7} \left(3 - \frac{j}{7}\right)^2$

Would you like more details on how I derived this notation, or do you have any questions?

Here are some related questions to explore further:

1. What are the properties of sigma notation in summing series?
2. How can this expression be expanded term-by-term?
3. What does it mean to square each term inside a summation?
4. How does changing the upper bound of $j$ affect the sum?
5. How could this sum be approximated or simplified for large bounds?

Tip: When writing in sigma notation, always identify a pattern in each term and the range of values for the index to make the expression concise and accurate.