Description
Form a one-sided next-term enclosure for a supplied alternating-series partial sum.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Form a one-sided next-term enclosure for a supplied alternating-series partial sum.
When to use this tool
Use it for alternating series next term bound when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter partialSum, nextMagnitude, nextPositive. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read lower, upper. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Form a one-sided next-term enclosure around partialSum using a nonnegative nextMagnitude. If the next term is positive, return partialSum through partialSum+nextMagnitude; otherwise return partialSum-nextMagnitude through partialSum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| partialSum | Partial Sum | Required. Finite number. |
| nextMagnitude | Next Magnitude | Required. Finite number; minimum 0. |
| nextPositive | Next Positive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
{
"input": {
"partialSum": 2,
"nextMagnitude": 0.1,
"nextPositive": false
},
"output": {
"lower": 1.9,
"upper": 2
}
}Limitations and assumptions
- The alternating-series interpretation requires alternating signs and subsequent magnitudes decreasing to zero. Those assumptions are supplied rather than checked from actual terms.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For alternating series next term bound, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Geometric Series Single Tail Bound
Calculate an absolute tail bound from a first omitted magnitude and a supplied geometric domination ratio.
- Alternating Prefix Balance
Calculate the signed unit-term balance in an alternating prefix.