The reason I didn't multiply 4 and 13 directly is because the summation notation represents the sum of multiple terms, each of which is \(4Y_i\) where \(i\) ranges from 1 to 13. 

Here’s why:

1. **Sigma Notation Basics**: The sigma (∑) notation is used to represent the sum of a sequence of terms. In your case, the expression \( \sum_{i=1}^{13} 4Y_i \) means that for each value of \(i\) from 1 to 13, you take the term \(4Y_i\) and sum them all together.

2. **Term-by-Term Addition**: The notation implies that \(4Y_1 + 4Y_2 + \cdots + 4Y_{13}\) are all added together. Multiplying 4 by 13 would not account for the summation of the individual \(Y_i\) terms but rather would incorrectly assume that all the \(Y_i\) values are equal to 1.

However, if all the \(Y_i\) values were indeed equal to a constant \(Y\), then the sum could be simplified. In that case, the expression would become:

\[
\sum_{i=1}^{13} 4Y = 4Y \times 13 = 52Y
\]

But in the general case, each \(Y_i\) could be different, so the summation must be carried out individually over all terms.

Would you like more details or have further questions?

Here are some follow-up questions:

1. What happens if the sequence \(Y_i\) has a known pattern (e.g., arithmetic or geometric)?
2. How would the summation change if \(Y_i\) was replaced with a specific function of \(i\)?
3. Can you factor out constants from a summation, and under what circumstances?
4. What would the result be if \(Y_i\) were all equal to 1?
5. How would you apply this summation in a practical scenario, like calculating the total cost of items?

**Tip:** Always double-check whether the terms inside the summation are constants or variables before simplifying the expression.

Explore the intricacies of summation notation with a focus on why 4 and 13 weren't multiplied directly. This detailed explanation covers the basics of sigma notation, term-by-term addition, and scenarios where constants versus variables impact summations.

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