Sigma Notation

Sigma notation is a way to represent the summation of a series of numbers. It uses the Greek letter Σ (sigma) to indicate a sum.

General Form

The general form of sigma notation is:

Where:

• i: The index of summation, which changes value from the lower limit (m) to the upper limit (n).
• f(i): The function to sum.

Interactive Example

Sigma Notation

Sigma notation is a mathematical way to represent the summation of a series of terms. It uses the Greek letter Σ to denote the sum.

General Form

Where:

• i: Index of summation.
• m: Lower limit of summation.
• n: Upper limit of summation.
• f(i): Function of the summation variable i.

Examples

Summation of Integers

Calculate Σi=15 i:

Summation of Squares

Calculate Σi=14 i2:

Properties of Summation

• Linearity: Σ(a*f(i) + b*g(i)) = a*Σf(i) + b*Σg(i)
• Constant Factor: Σk = k*(n-m+1) where k is constant.
• Distributive: Σ(f(i) + g(i)) = Σf(i) + Σg(i)

Applications of Sigma Notation

• Finding sums of arithmetic and geometric sequences.
• Expressing series in compact form.
• Calculating areas under curves (in calculus).
• Computer algorithms and loop-based computations.