Sigma Notation (Summation) Calculator
Add up an expression in i from a start value to an end value, with the first terms shown.
Sum
385
- Notation
- Σ i^2, i = 1 to 10
- First terms
- 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + …
- Number of terms
- 10
- Average term
- 38.5
The sum is 385.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Number of terms | 10 − 1 + 1 | 10 |
| Sum | Add i^2 for every whole i from the start to the end | 385 |
How it works
Type the expression in i, then the start and the end value of i.
Worked example
Σ i² for i = 1 to 10:
- Terms: 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
- Number of terms: 10 − 1 + 1 = 10
- Sum: 385, an average of 38.5 per term
Sources
Frequently asked questions
What does sigma notation mean?
The Greek letter sigma, Σ, means add up. Below it is the starting value of i and above it the ending value. You work out the expression for each whole number of i in that range and add the results. Σ i² for i = 1 to 4 is 1 + 4 + 9 + 16 = 30.
How do I type the expression?
Use the letter i with + − * / ^ and parentheses, such as i^2, 2^i or (2*i + 1). Write 2*i, not 2i, because the calculator does not guess the multiplication.
What are some sums I can check?
Adding 1 to 100 gives 5,050, a result attributed to Gauss. The sum of i² from 1 to 10 is 385, and the sum of 2^i from 0 to 10 is 2,047.
How many terms can I add?
Up to 10,000. A larger range is rejected. For an endless geometric series, use the geometric sequence calculator.
Can the start be negative?
Yes, as long as it is a whole number and not greater than the end. Σ (2*i + 1) from i = −2 to 2 adds the five terms −3, −1, 1, 3, 5 to get 5.