Summation Calculator

Calculate the sum of a sequence using sigma notation.

Calculator

Enter Your Expression

Enter a mathematical expression using 'n' as the variable (e.g., n^2 + 2*n + 1)

Concept

Summation Formula

The summation (sigma notation) represents the sum of a sequence of terms. It is denoted by the Greek letter sigma (Σ).

Formula:
Σ(n=a to b) f(n) = f(a) + f(a+1) + ... + f(b)
Steps

How to Calculate Summation

To calculate a summation, follow these steps:

  1. 1
    Enter the expression using 'n' as the variable
  2. 2
    Specify the start value (lower bound)
  3. 3
    Specify the end value (upper bound)
  4. 4
    Calculate the sum of all terms from start to end

For example, to find the sum of n² from 1 to 5:

Example Calculation:
Σ(n=1 to 5) n² = 1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55
Examples

Summation - Practical Examples

Example 1 Sum of Natural Numbers

Calculate the sum of natural numbers from 1 to 10.

Σ(n=1 to 10) n = 1 + 2 + 3 + ... + 10 = 55

Example 2 Sum of Squares

Calculate the sum of squares from 1 to 5.

Σ(n=1 to 5) n² = 1² + 2² + 3² + 4² + 5² = 55

Example 3 Arithmetic Sequence

Calculate the sum of the arithmetic sequence 2n + 1 from 1 to 5.

Σ(n=1 to 5) (2n + 1) = (2*1 + 1) + (2*2 + 1) + ... + (2*5 + 1) = 35

Tools

Mathematics Calculators

Need other tools?

Can't find the calculator you need? Contact us to suggest other mathematical calculators.