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Math Help - Converging of Digits proof

  1. #1
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    Converging of Digits proof

    Let (d sub k) from k=1 to inf be a sequence of digits. Then

    Summation from j=1 to inf { (d sub j) * (10^-j) } converges.


    Any idea on how to complete this proof? Any help is appreciated!
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  2. #2
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    Quote Originally Posted by jstarks44444 View Post
    Let (d sub k) from k=1 to inf be a sequence of digits.


    So \{d_k\}_{k=1}^\infty\,,\,\,d_k=0,1,2,...,9\,\,\for  all k


    Then

    Summation from j=1 to inf { (d sub j) * (10^-j) } converges.


    Then \displaystyle{\sum\limits^\infty_{k=1}\frac{d_k}{1  0^k}} converges

    Any idea on how to complete this proof? Any help is appreciated!

    The series is an infinite positive one, so why don't you try to bound it up from above...say, by a converging geometric series...?

    Tonio
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