The symbol ∑ is called the summation symbol, also known as sigma notation. It's a shorthand way to represent the sum of a series of numbers or terms that follow a pattern.
Understanding Summation Notation
Summation notation uses the Greek capital letter sigma (Σ) to concisely express a sum. The notation typically includes:
- The summation symbol: Σ
- The index of summation: A variable (often i, j, or k) that represents the current term in the sequence.
- The lower limit of summation: The starting value of the index.
- The upper limit of summation: The ending value of the index.
- The expression to be summed: The formula or rule that generates each term in the sequence.
Example:
The expression ∑_{i=1}^{5} i represents the sum of integers from 1 to 5: 1 + 2 + 3 + 4 + 5 = 15.
Several sources confirm this:
- Math Insight: Describes Σ as indicating summation and being used as shorthand for the sum of terms following a pattern.
- MathBitsNotebook: Refers to the notation as "summation notation" or "sigma notation."
- Wikipedia: Defines summation as the addition of a sequence of numbers.
- Khan Academy: Explains that the sigma symbol (∑) indicates summation.
- Various Quora answers: Clearly state that ∑ is the summation symbol.
- Cuemath: Refers to it as sigma notation and summation notation.
The symbol's use extends beyond basic arithmetic, appearing in various mathematical contexts like series, calculus, and statistics. Understanding summation notation is crucial for efficiently representing and manipulating sums of many terms.
