Sigma Notation Calculator: Clear, Accurate Summation

This sigma notation calculator sums a formula across integer values of i.

The parser now reads common math syntax and computes each series correctly.

Enter your expression and set the bounds.

Click Calculate Sum to see the sigma line and the total.

It also lists every term.

A short syntax guide with examples helps you write valid input fast.

Why You'll Love Using It

Students and teachers use this sigma notation calculator to check work.

Engineers and analysts use it for quick sums.

It shows each term so you follow the math with ease.

Results appear fast and the layout stays clear.

• Quick checks for homework and exams
• Step lists that aid tutoring and study
• Clean sums for reports and notes
• Support for common math functions and constants

How It Works

Type a formula that uses the index i.

Set a start value and an end value.

The calculator sums the formula for each integer from start to end.

Both bounds are included in the sum.

Results show the sigma line and the final total.

You also see each step.

• Expression: enter a formula that uses i as the index
• Lower Bound: enter the starting integer for i
• Upper Bound: enter the ending integer for i

Supported syntax at a glance:

• Basic operators: + - * / and parentheses
• Powers: use ** or use ^ or call Math.pow with base and exponent
• Functions: sqrt abs floor ceil round sin cos tan
• Math prefixes work too like Math.sqrt and Math.abs
• Logs: log gives the natural log
• Log base ten: use log10
• Exponential: use exp
• Constants: use pi or the symbol π
• Euler's number: use e
• You can also use Math.PI and Math.E

What the output means:

• Result: the final sum across the full range
• Sigma notation: the compact form with Σ and bounds
• Calculation steps: a line for each i with the value
• Summary line: shows the first few and the last few terms

Notes and limits:

• Bounds accept integers only
• The lower bound is less than or equal to the upper bound
• The range allows up to 1000 terms
• A formula that lacks i repeats the same term each time
• Any invalid term stops the run and shows an error
• You can press Enter in any field to run the sum

Your Step-by-Step Guide

1. Write your sigma expression with i as the index.
2. Enter the starting integer in Lower Bound.
3. Enter the ending integer in Upper Bound.
4. Click Calculate Sum or press Enter.
5. Review the sigma line and the steps and the result.

Benefits You Can Count On

This sigma notation calculator helps with study and research.

It also supports quick checks.

You get clear steps and a clean total.

• Verify a known formula with numbers
• Compare partial sums for growth
• Explore arithmetic or geometric sequences
• Check cases that use negative bounds
• Build quick examples for class
• Prepare a study sheet with worked sums

Example expressions you can try:

• i**2 gives the sum of squares
• 2*i + 1 gives the sum of odd numbers
• 1/i gives a partial harmonic sum
• i*(i+1)/2 gives the sum of triangular numbers
• sqrt(i) gives a sum of square roots
• 3**i gives a geometric series sum

Start with a small range and check the steps.

Grow the range once you like the result.

Keep syntax simple for smooth runs.