Calculator
Example Data Table
| Listed Terms | Pattern | Sigma Notation | Sum |
|---|---|---|---|
| 3, 6, 9, 12, 15 | Arithmetic | Σ_{n=1}^{5} (3n) | 45 |
| 5, 10, 20, 40 | Geometric | Σ_{n=1}^{4} (5·2^(n-1)) | 75 |
| 1, 4, 9, 16 | Power | Σ_{n=1}^{4} (n^2) | 30 |
| 2, 5, 10, 17 | Quadratic | Σ_{n=1}^{4} (n^2 + 1) | 34 |
Formula Used
Sigma notation writes repeated addition with one compact summation rule.
General form: Σ_{n=m}^{N} f(n)
Here, m is the starting index, N is the ending index, and f(n) is the term formula.
Arithmetic series: Σ_{n=m}^{N} [a₁ + (n - m)d]
Geometric series: Σ_{n=m}^{N} [a₁r^(n - m)]
Linear terms: Σ_{n=m}^{N} (an + b)
Quadratic terms: Σ_{n=m}^{N} (an² + bn + c)
Power terms: Σ_{n=m}^{N} (a·n^p)
The calculator builds f(n), expands the terms, and totals the numeric sum.
How to Use This Calculator
- Choose auto-detect mode for listed terms or builder mode for manual rules.
- Enter the starting index. Builder mode also needs an ending index.
- For auto-detect mode, paste comma-separated terms like 3, 6, 9, 12.
- For builder mode, select arithmetic, geometric, linear, quadratic, power, or custom.
- Enter the needed coefficients, ratio, difference, exponent, or custom formula.
- Click the calculate button to generate the sigma rule above the form.
- Review the graph, term table, expanded sum, and total value.
- Use the export buttons to save the output as CSV or PDF.
FAQs
1) What does this calculator do?
It converts repeated terms into compact sigma notation. You can auto-detect common patterns from a list or build notation manually using arithmetic, geometric, polynomial, power, or custom formulas.
2) How do I enter a sum from listed terms?
Enter listed terms for auto-detection or choose builder mode. Then set the start and end indices, review the generated sigma expression, and download the table if needed.
3) What does the graph show?
Yes. The graph plots each term against its index. This helps you inspect growth, direction, and spacing before using the sigma expression elsewhere.
4) Which patterns can auto-detection recognize?
Auto-detection is strongest for arithmetic, geometric, linear, quadratic, and simple power patterns. Irregular sequences may need builder mode or a custom formula.
5) How should I write a custom formula?
Use explicit multiplication, such as 3*n+1 or 2*(n^2). The calculator accepts numbers, parentheses, n, and basic operators.
6) What is the computed sum value?
The sum value is the numeric total after evaluating every generated term from the starting index through the ending index.
7) What do the CSV and PDF files include?
CSV exports the index and term table. PDF exports the detected pattern, sigma notation, expanded sum, total, and table summary.
8) Can I adjust the bounds and formula quickly?
Yes. Change the variable symbol, bounds, or formula inputs, then submit again. The result section updates above the calculator form.