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THE FEUTEX TOOLKIT

Three-Level Continued Fraction

Evaluate a short continued fraction and its exact numerator-denominator recurrence.

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02 Your result
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FormulaNumerator = a0*(a1*a2*a3+a1+a3)+a2*a3+1; Denominator = a1*a2*a3+a1+a3; Value = a0+1/(a1+1/(a2+1/a3))
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Made for real tasks

  • Evaluate a short continued fraction and its exact numerator-denominator recurrence.
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Worked example

Inputs

Integer part
1 count
First denominator
2 count
Second denominator
2 count
Third denominator
2 count

Expected results

Numerator
17 number
Denominator
12 number
Value
1.416666667 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter integer part, first denominator, second denominator, third denominator.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a0": 1,
  "a1": 2,
  "a2": 2,
  "a3": 2
}

Accuracy and scope

Simple continued fraction [a0;a1,a2,a3]; numerical recurrence remains within safe integer range for the supplied bounds.

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