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Value of an infinite continued fraction with a repeating pair of terms

The same question, asked 2 times: 2021 Paper 7*, 2021 Paper 9. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 7

    76
    The value of 4+15+14+15+14+⋯4 + \cfrac{1}{5 + \cfrac{1}{4 + \cfrac{1}{5 + \cfrac{1}{4 + \cdots}}}} (continued infinitely with the period 4, 5) is:

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  2. Question 2

    2021 Paper 9

    80
    The value of 3+14+13+14+13+…∞3 +\frac{1}{4 +\frac{1}{3 +\frac{1}{4 +\frac{1}{3 + \ldots\infty}}}} is equal to

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