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Math Help - Limit of sequence

  1. #1
    Len
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    Limit of sequence



    This sequence is strictly increasing (monotonic, already proved).

    3 is an upper bound on this sequence(already proved). Therefore I know that this sequence converges to a Limit A which is <= 3.

    My question is knowing all this, how do I find the Limit A? I.E. What the series converges to, the exact number.

    Thanks,

    Len
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Len View Post


    This sequence is strictly increasing (monotonic, already proved).

    3 is an upper bound on this sequence(already proved). Therefore I know that this sequence converges to a Limit A which is <= 3.

    My question is knowing all this, how do I find the Limit A? I.E. What the series converges to, the exact number.

    Thanks,

    Len
    Let \lim b_n = L. then, of course, \lim b_{n + 1} = L as well.

    thus, take b_{n + 1} = 3 - \frac 1{b_n}

    take the limit of both sides.

    \lim b_{n + 1} = \lim \left(3 - \frac 1{b_n} \right)

    \Rightarrow L = 3 - \frac 1L

    i leave the rest to you
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