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Math Help - convergence of a series

  1. #1
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    convergence of a series

    How would I go about checking the convergence (absolute/conditional) of:
    convergence of a series-untitled.png

    Thank you
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hints :

    (i) Decompose:

    (\sin 3n)(\cos n)=\dfrac{1}{2}(\sin 4n+\sin 2n)

    (ii) Use the Dirichlet test.


    Fernando Revilla
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  3. #3
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    What about this one?

    convergence of a series-untitled.png

    Tried to divid by 1/n and 1/n^2 but couldn't find a finit limit.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Hints :


    \sin \dfrac{1}{\sqrt{n}}\sim \dfrac{1}{\sqrt{n}}\;(n\rightarrow +\infty)

    \log \dfrac{n+1}{n-1}=\log\left(1+\dfrac{2}{n-1}\right)\sim \dfrac{2}{n-1}\; (n\rightarrow +\infty)

    P.S. Perhaps, it should be better to open new threads for new problems. Thanks.


    Fernando Revilla
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