Final answer:
Sigma notation is a concise way to represent summation of a series of terms, utilizing the Greek letter sigma (Σ) to indicate the sum. It includes expressions for terms, an index, and upper and lower bounds. For example, the sum of the first five positive integers in sigma notation is Σi=15 i.
Step-by-step explanation:
To express a given sum using sigma notation, we use the Greek letter sigma (Σ), which indicates that a series of terms are to be added together. The sigma notation includes an expression for the terms to be added, an index of summation (often i, j, or another variable), a lower bound (where the index starts), and an upper bound (where the index ends).
For example, to add the first five positive integers, we would write: Σi=15 i, which translates to 1 + 2 + 3 + 4 + 5. In the context of the question, if we are summing the products of midpoints and frequencies, we may have Σi=1n (midpoint_i × frequency_i), where 'n' is the number of midpoints and frequencies.
In examples relating to sigma notation in scientific contexts, we could see equations such as ΣX⁻, which refers to the sum over some variable X, with the negative exponent indicating a transformation such as the inversion of each term before summation.