Inputs
Finite series Sn
Tip: Press Enter to calculate
Results
Sn = ∑k=1..n a·rk-1Example data
Click a row to load| a | r | n | Description | |
|---|---|---|---|---|
| 2 | 0.5 | 6 | Halving sequence, six terms | |
| 5 | 2 | 4 | Doubling sequence, four terms | |
| 3 | -0.4 | 8 | Alternating decreasing magnitude |
Formula used
Sn = a + a r + a r2 + … + a rn-1
For r ≠ 1:
Sn = a (1 − rn) / (1 − r)
For r = 1:
Sn = a · n
k-th term:
tk = a · rk-1
This tool auto-detects r close to 1 and uses the appropriate formula to stabilize rounding.
How to use this calculator
- Enter the first term a, the common ratio r, and the number of terms n.
- Adjust decimal places and display formatting as needed.
- Click Calculate to compute Sn, the last term, and more.
- Enable the partial sums table to view k, term, and Sk.
- Use Download CSV or Download PDF to export your results.
FAQs
The sum simplifies to Sn = a·n because every term equals a.
Yes. Terms alternate in sign when r < 0. The same formulas apply.
You can choose rounding from 0–12 decimals. Internally, calculations use double-precision floating point.
Large n can produce very big or tiny numbers. The tool warns about extremely large tables and may truncate the preview.
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