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Math Help - Iteration formula converges to 1 recurring

  1. #1
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    Iteration formula converges to 1 recurring

    I am just wondering - is there an iteration formula that converges to 1 recurring?

    (not 0.11111111111 but 11111111111)

    Not simply by saying 111111111 = infinity and then find one that keeps expanding, Im looking for

    x0=1
    x1=11
    x2=111

    etc.

    Bit of a wierd question I know - But if anyone could show me a way (although I doubt that its possible) Id be very thankful Thanks
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  2. #2
    MHF Contributor

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    Do you mean x_{n+1}=10x_n+1? (this sequence diverges to +\infty; however, one could say that the sequence of its digits converges to a sequence of 1's)
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  3. #3
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    Aha well this is embarrassing...

    ive been working on this for ages doing really stupidly complex stuff.

    Facepalm.

    Thanks anyway lol
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