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Math Help - a_0 might be 0, but a_1 cannot be 0

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    Question a_0 might be 0, but a_1 cannot be 0

    Here is another question of continued fraction which I got stuck with.

    Question : a_0 might be 0, but a_1 cannot be 0
    a_n for positive n must be strictly positive, but a_0 may be zero. Construct an example(i.e. specific a_n for which a_0 = 0 ). Explain the geometric significance of what you've done.

    Please teach me how to solve it. Thank you very much.
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  2. #2
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    Quote Originally Posted by beta12 View Post
    Here is another question of continued fraction which I got stuck with.

    Question : a_0 might be 0, but a_1 cannot be 0
    a_n for positive n must be strictly positive, but a_0 may be zero. Construct an example(i.e. specific a_n for which a_0 = 0 ). Explain the geometric significance of what you've done.

    Please teach me how to solve it. Thank you very much.
    All this is saying is that continued fraction has the form,
    [A;B,C,D,E,...]
    Where,
    B,C,D,E,... are all positive integers.
    While,
    'A' can be any integer (also negative).

    The reason why is that if we let one of the B,C,D,E,... be zero it might let to division by zero .

    The rule with these continued fractions is that they are between 0 and 1.
    Meaning any continued fraction you chose with the first term being zero, its values will not exceede 1.
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