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Continued fraction: simplify from the bottom up

This type of question, asked 3 times: 25 Jul 2023 S1, 12 Sep 2025 S2, 15 Sep 2025 S3. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jul 2023 S1

    60
    What value of 'y' will satisfy the following equation? 3y1+11+y1−y=2\frac{3y}{1 + \frac{1}{1 + \frac{y}{1 - y}}} = 2

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  2. Question 2

    12 Sep 2025 S2

    53
    Evaluate the continued fraction: x=2+13+14+12x = 2 + \frac{1}{3 + \frac{1}{4 + \frac{1}{2}}}

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  3. Question 3

    15 Sep 2025 S3

    53
    Which of the following represents the correct simplified value of the continued fraction:x=1+12+12+12x = 1 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2}}}

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