Math
Master the quantitative skills used in science and healthcare: significant figures, unit conversions, proportions, functions, exponents, logarithms, statistics, and introductory calculus.
Sigma Notation
Sign in to track progressSigma notation provides a compact way to write sums. It is widely used in statistics, calculus, and numerical methods.
Sigma Notation The Greek letter Σ (capital sigma) means "sum." The expression
Σᵢ₌₁ⁿ aᵢ
means "add up the terms aᵢ for i = 1 to n."
Parts of Sigma Notation
Σ = summation sign
i = index of summation
1 = lower bound (starting value)
n = upper bound (ending value)
aᵢ = expression to evaluate at each value of i
Evaluating Finite Summations Write out the terms and add them.
Example: Σᵢ₌₁³ i = 1 + 2 + 3 = 6
Sum of Squared Terms Sigma notation is especially useful for sums of squares, which appear in statistics and regression.
Example: Σᵢ₌₁³ i² = 1² + 2² + 3² = 1 + 4 + 9 = 14
Common Summation Formulas
Σᵢ₌₁ⁿ i = n(n+1)/2
Σᵢ₌₁ⁿ i² = n(n+1)(2n+1)/6
Σᵢ₌₁ⁿ c = c·n (where c is a constant)
Key Points
- Σ means 'sum' in sigma notation
- The index runs from the lower bound to the upper bound
- Evaluate a summation by writing out each term and adding
- Sum of squared terms appears frequently in statistics
- Standard formulas exist for sums of integers and squares