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Math Help - q_1, q_2, ... , q_n, ... is a sequence of real numbers

  1. #1
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    q_1, q_2, ... , q_n, ... is a sequence of real numbers

    q_1, q_2, ... , q_n, ... is a sequence of real numbers such that the limit of q_n, as n goes towards infinity, is +infinity.

    Show that we can find a sequence a_1, a_2, ... , a_n, ... sych that the sum(a_n) is convergent but the sum(a_n*q_n) is divergent.
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  2. #2
    Super Member girdav's Avatar
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    We can find a stricly increasing sequence of integer (n_k) such that q_{n_k}\geq k. Put a_{n_k}=1/(kq_{n_k}) and a_j=0 if j\neq n_k for all k.
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  3. #3
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    What is geq and neq
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by ahm0605 View Post
    What is geq and neq

    Greater or equal and not equal .
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  5. #5
    Super Member girdav's Avatar
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    Quote Originally Posted by ahm0605 View Post
    What is geq and neq
    I will edit this post when LaTeX will work. I hope it's understandable.
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  6. #6
    Super Member girdav's Avatar
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    Well I write again my first post.
    We can find a strictly increasing sequence of integer (n_k) such that q_{n_k}\geq k. Put a_{n_k}=\frac 1{kq_{n_k}} and a_j=0 if j\neq n_k for all k.
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