Sigma Notation Calculator

About Sigma Notation Calculator

Sigma notation (Σ) is a compact way to write sums. The variable iterates from the lower to upper bound.

How to use this calculator

1. Enter the expression for the terms in the sum, such as \(i^2\) or \(3i+1\).
2. Set the lower index, which is the starting value of the variable, such as \(i=1\).
3. Set the upper index, which is the last value of the variable, such as \(n=5\).
4. Evaluate the sum to get the total of all terms from the start to the end.

The formula explained

The formula \(\sum_{i=1}^{n} f(i)\) means add the values of \(f(i)\) for every integer \(i\) from 1 up to \(n\). It computes a finite sum built from a rule or pattern.

• i = the index variable that changes through the terms of the sum
• n = the upper limit, or the last value included in the sum
• f(i) = the expression for each term in the sum

Step by step method

1. Replace the index \(i\) with the first value and find the first term.
2. Continue substituting each whole number up to the upper limit.
3. Add all the terms together to get the total.

Worked example

Problem. Evaluate \(\sum_{i=1}^{5} (2i+1)\).

1. List the terms: when \(i=1,2,3,4,5\), the values are \(3, 5, 7, 9, 11\).
2. Add them: \(3+5+7+9+11=35\).
3. So the sum of the five terms is 35.

Tips and common mistakes

• Make sure the index starts and ends at the correct values, because changing either one changes the total.
• If the expression has parentheses or powers, keep them in place when you substitute values, such as using \((2i+1)\) exactly as written.

Frequently asked questions