Sigma Notation Calculator

How to Use:

Enter a mathematical expression using 'i' as the index variable. The calculator will compute the sum of this expression for all integer values of i from the lower to upper bound.

Supported Syntax:

  • Basic operators: + - * / ( )
  • Exponents: Use ** or Math.pow(base, exp)
    Examples: i**2 or Math.pow(i, 2) for i²
  • Common functions: Math.sqrt(i), Math.abs(i), Math.floor(i), Math.ceil(i)
  • Constants: Math.PI, Math.E

Example Expressions:

  • i**2 → Sum of squares
  • 2*i + 1 → Sum of odd numbers
  • 1/i → Harmonic series
  • i*(i+1)/2 → Sum of triangular numbers
  • Math.sqrt(i) → Sum of square roots

Result: —

Calculation Steps:

This tool sums a mathematical expression using sigma notation. It uses the letter i as the index variable and computes the sum from a lower bound to an upper bound.

How to Use This Tool

Follow these steps:

  1. Type your sigma expression in the first box. Use the letter i as your index. For example, type i**2 for i squared.
  2. Enter the starting number in the lower bound field.
  3. Enter the ending number in the upper bound field. The upper value must be equal to or more than the lower value.
  4. Click the Calculate Sum button.

Understanding the Input Fields

The expression field is where you write your math expression. Use operators like +, -, *, / and functions such as Math.sqrt or Math.abs. The calculator works with these standard operations.

The lower bound field is for the start value. This must be an integer.

The upper bound field is for the end value. This must also be an integer. The tool performs a maximum of 1000 iterations to keep things fast.

Interpreting the Output

After you click Calculate Sum, the tool shows the final total. A step-by-step breakdown is also displayed. This section shows how each term of the sum is calculated.

The sigma notation line at the top gives a quick glance of the overall calculation.

Limitations and Special Notes

The calculator runs expressions with standard math functions. It supports exponentiation with double asterisks or Math.pow. It does not produce graphics or plots.

When using large ranges, be sure that the difference between the lower and upper bound does not exceed 1000 steps.

Examples of Common Use Cases

Students often use this tool for homework and exam preparation. It makes checking sums easier.

For instance, input i**2 and set the lower value to 1 and the upper value to 5. The tool then calculates and shows the sum of the squares.

You might try an expression like 2*i+1 to add up a series of odd numbers.