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Math Help - a_{n+1}=a_n+1/S_n - sequence, limit

  1. #1
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    a_{n+1}=a_n+1/S_n - sequence, limit

    a_1=1, a_{n+1}=a_n+\frac 1{S_n} where n=1,\,2,\ldots and S_n=a_1+a_2+\ldots +a_n. Prove that \lim_{n\rightarrow\infty}a_n=\infty. Take b_n=n(a_n^2-a_{n-1}^2); does it have a limit if yes what?
    Last edited by james_bond; October 9th 2009 at 09:16 AM. Reason: Corrected an error in the statement.
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    Quote Originally Posted by james_bond View Post
    a_1=1, a_{n+1}=a_n+\frac 1{S_n} where n=1,\,2,\ldots and S_n=a_1+a_2+\ldots +a_n. Prove that \lim_{n\rightarrow\infty}a_n=0.
    That is impossible. \left(a_n\right) is clearly increasing and each term is \ge 1.
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  3. #3
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    Quote Originally Posted by Plato View Post
    That is impossible. \left(a_n\right) is clearly increasing and each term is \ge 1.
    I'm sorry. My bad. Corrected it!
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