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Math Help - Convergence of a series

  1. #1
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    Convergence of a series

    Ok so i am looking for a series convergent for An but noy convergent for Akn (k>1 and integer) for example:


    a1+a2+a3+a4+a5+.... is convergent

    but a2+a4+a6+a8 .... and a3+a6+a9+a12+.... are not convergent


    I know that I need negative terms
    I have tried using alternating harmonic series while that works for a2+a4+a6
    it doesnt work for a3+a6+a9.. so i need a bit tweaking somewhere there but i dont know what to do/change

    also another question i have is:
    Does adding 2 convergent series together always produce a convergent one ?
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  2. #2
    Grand Panjandrum
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    Re: Convergence of a series

    Quote Originally Posted by armansuper View Post
    Does adding 2 convergent series together always produce a convergent one ?
    Subtracting the alternating harmonic series from twice the alternating harmonic series term by term gives the harmonic series.



    CB
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