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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.

Use sigma notation to write the sum: [3 - (1/7)]^2 + [3 - (2/7)]^2 + ... + [3 - (7/7)]^2

Learn to express a series as a sigma notation: [3 - (1/7)]^2 + [3 - (2/7)]^2 + ... + [3 - (7/7)]^2. This solution covers key concepts like summation notation, series, and exponents, and provides a step-by-step breakdown for students in Grades 9-11.

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