To write the series $-2, -1, 0, 1, 2, 3, 4, 5$ in sigma notation, we need to express it as a summation over a range of values of $n$.

1. The series can be represented as:

$\sum_{n=1}^{7} (n - 3)$

Explanation:

• The series starts with $n=1$, and we want to shift the values so that when $n=1$, we get $-2$.
• The pattern follows the formula $n - 3$. So when $n=1$, the term is $1 - 3 = -2$, when $n=2$, the term is $2 - 3 = -1$, and so on.
• The summation runs from $n=1$ to $n=7$ to cover all the terms.

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Related questions:

1. How do you determine the general formula for a sequence in sigma notation?
2. How do you transform a sequence with a constant term into sigma notation?
3. What are other common ways to represent series and sequences in mathematical notation?
4. How can I find the sum of a series using sigma notation?
5. What is the difference between a finite and an infinite series in sigma notation?

Tip:

When writing series in sigma notation, always ensure the index corresponds to the correct first and last terms of the sequence. Adjust the formula so that it generates the correct terms.