Description
Advance one harmonic-progression term by a supplied increment in reciprocal space.
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.
Advance one harmonic-progression term by a supplied increment in reciprocal space.
When to use this tool
Use it for harmonic progression reciprocal step when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter current, reciprocalDifference. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read next. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Advance a harmonic progression by adding reciprocalDifference to 1/current and taking the reciprocal again. The difference has inverse-term units; a nonzero current and nonzero resulting reciprocal are required.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| current | Current | Required. Finite number. |
| reciprocalDifference | Reciprocal Difference | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| next | Next | Required. Finite number. |
{
"input": {
"current": 0.5,
"reciprocalDifference": 1
},
"output": {
"next": 0.3333333333333333
}
}Limitations and assumptions
- This advances one caller-established progression and does not fit a sequence. Cancellation near zero can produce a very large result; nonfinite output is rejected.
- 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 harmonic progression reciprocal step, 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
- Arithmetic Progression Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.
- Affine Recurrence Two Step Constant
Return the coefficients obtained by composing a supplied affine recurrence twice.