Enter Polynomial Series Inputs
Define coefficients for P(n) = a₀ + a₁n + a₂n² + ... + a₈n⁸, then choose the finite range and step size.
Example Data Table
Sample polynomial: P(n) = 2 - n + 3n2
| # | n | P(n) | Cumulative Sum |
|---|---|---|---|
| 1 | 1 | 4 | 4 |
| 2 | 2 | 12 | 16 |
| 3 | 3 | 26 | 42 |
| 4 | 4 | 46 | 88 |
| 5 | 5 | 72 | 160 |
Formula Used
Polynomial term formula:
P(n) = a₀ + a₁n + a₂n² + a₃n³ + ... + a₈n⁸
Finite series formula:
S = Σ P(nk) for k = 0 to m, where nk = start + k × step
How the result is computed:
- Each sequence point is generated from the chosen start, end, and step.
- The calculator evaluates the polynomial at every point using Horner’s method.
- All term values are added to produce the total finite series sum.
- Cumulative totals are stored to build the table and graph.
How to Use This Calculator
- Enter the polynomial coefficients from a₀ through a₈.
- Set the start value, end value, and positive step size.
- Choose the number of decimal places for displayed results.
- Press Calculate Series to compute the finite sum.
- Review the summary cards, result table, and Plotly graph.
- Use the CSV or PDF buttons to export the current output.
Frequently Asked Questions
1) What does this calculator solve?
It evaluates a polynomial across a finite sequence and adds those terms. You also get a table, cumulative totals, summary metrics, and a graph.
2) Can I use negative coefficients?
Yes. Every coefficient can be positive, negative, or zero. This allows rising, falling, and mixed polynomial behavior across the selected range.
3) Does the step size need to be 1?
No. You can use any positive step size, including decimals. The calculator treats each generated point as one term in the finite series.
4) Why is my term count smaller than expected?
The count depends on start, end, and step size. If the step skips values or the end is reached quickly, fewer terms are generated.
5) What is the cumulative sum column?
It shows the running total after each term is added. This helps you see how quickly the finite series grows, falls, or changes direction.
6) Why is there a row limit on screen?
Large tables can slow the page and reduce readability. The screen view is trimmed, but the CSV export still carries the full result set.
7) Is this only for integer inputs?
No. Coefficients, bounds, and step size may include decimals. The sequence points can therefore be non-integer values as well.
8) What graph is displayed?
The chart plots polynomial term values and cumulative sums against the generated sequence points. It helps compare local behavior with overall growth.