Sigma ($\Sigma$) is the Greek letter used to represent the sum of a sequence of terms. In mathematics, it is commonly used in summation notation to denote the sum of terms from a given sequence.
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The general form of sigma notation is $\Sigma_{i=a}^{b} f(i)$, where $i$ is the index of summation, $a$ is the lower limit, and $b$ is the upper limit.
Sigma notation can represent both finite and infinite series.
The expression inside the sigma notation can be a simple number, variable, or more complex function.
To evaluate a sigma notation for a finite series, substitute each integer value from $a$ to $b$ into the expression and sum the results.
Properties such as linearity hold for summations: $\Sigma (af(i) + bg(i)) = a \Sigma f(i) + b \Sigma g(i)$.
Review Questions
What does the symbol $\Sigma$ represent in mathematical notation?
How would you write the sum of integers from 1 to n using sigma notation?
What property allows you to split sums in sigma notation into multiple parts?