Calculator Inputs
Choose a supported series type, enter values, and calculate instantly.
Example Data Table
| Series Type | Example Inputs | Series Preview | Expected Sum |
|---|---|---|---|
| Arithmetic | a = 2, d = 3, n = 5 | 2, 5, 8, 11, 14 | 40 |
| Geometric | a = 3, r = 2, n = 4 | 3, 6, 12, 24 | 45 |
| Alternating Geometric | a = 5, r = 2, n = 4 | 5, -10, 20, -40 | -25 |
| Harmonic | start = 1, end = 4 | 1, 1/2, 1/3, 1/4 | 2.0833 |
| Squares | n = 4 | 1, 4, 9, 16 | 30 |
| Power | start = 1, end = 4, p = 3 | 1³, 2³, 3³, 4³ | 100 |
Formula Used
Arithmetic Series
S_n = n/2 × [2a + (n - 1)d]
Use this when each term increases or decreases by a fixed difference.
Geometric Series
S_n = a × (1 - r^n) / (1 - r)
Use this when each term is multiplied by the same ratio.
Alternating Geometric Series
S_n = a × [1 - (-r)^n] / (1 + r)
Use this when signs alternate and magnitudes follow a ratio.
Harmonic Series
S = Σ(1/k)
This tool computes finite harmonic sums between selected indices.
Natural Numbers
S_n = n(n + 1) / 2
Adds 1 through n with a standard closed-form expression.
Squares
S_n = n(n + 1)(2n + 1) / 6
Adds square values from 1² through n².
Cubes
S_n = [n(n + 1) / 2]²
Adds cube values from 1³ through n³.
Power Series
S = Σ(k^p)
Useful for flexible powered sums over a chosen range.
How to Use This Calculator
- Choose the series type from the dropdown list.
- Enter the values required for that specific formula.
- Set the number of decimal places you want displayed.
- Click the calculate button to process the series.
- Review the result box above the form.
- Check the term table and Plotly graph for deeper insight.
- Export the full calculation as CSV or PDF.
- Use the example table to test the calculator quickly.
FAQs
1. What does this calculator solve?
It computes finite sums for several common series, including arithmetic, geometric, harmonic, natural numbers, squares, cubes, and custom power sums.
2. Can I calculate an arithmetic series here?
Yes. Enter the first term, common difference, and number of terms. The tool applies the arithmetic sum formula and lists every generated term.
3. Can I calculate a geometric series too?
Yes. Provide the first term, common ratio, and total terms. The calculator returns the final sum, term table, and cumulative growth chart.
4. Why is there a harmonic option?
Harmonic sums appear in mathematics, algorithms, and analysis. This tool evaluates finite ranges, so you can study partial sums clearly.
5. What is the power series mode for?
It lets you sum values like k², k³, or k raised to another chosen exponent across a selected index range.
6. Does the graph show the final answer only?
No. The graph shows both individual term values and the cumulative sum. That helps you see how quickly totals grow.
7. What do the CSV and PDF exports include?
They include summary metrics, the selected formula, and the generated term table. This makes reporting and record keeping easier.
8. Is this calculator useful for learning?
Yes. It combines formulas, examples, tables, and a chart, so learners can connect symbolic rules with numeric results.