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Math Help - Two variables? Series involving x and n

  1. #1
    Newbie Thorpie09's Avatar
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    Exclamation Two variables? Series involving x and n

    Since I was quarantined due to the swine flu, I missed this part of my Calc 2 class. I've done some problems dealing with convergence and divergence of series, but I've never done one with two variables. Is there a certain way to go about it, or are there multiple ways? Which do you think is best?

    Such as

     \sum_{n=1}^{\infty}\frac{x^n}{5^n}

    or

     \sum_{n=0}^{\infty} (x+1)^{n}3^{n}

    I think I'm finally getting this Latex stuff down
    Thanks sooo much!
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  2. #2
    MHF Contributor chisigma's Avatar
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    properly speching, the expressions You have written are not 'simple series' but series of functions. The have the general form...

    \varphi (x)= \sum_{n} \varphi_{n} (x) (1)

    Such series converges for x in a given interval [a,b] and and there are two types of convergence...

    a) 'simple' convergence...

    b) uniform convergence...

    The full explanation is a little complex and can't be done in short notes. I'm shure that You will be able to 'recovery' the time lost during your illness...

    MHF is at Your disposition for that !...

    Kind regards

    \chi \sigma
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  3. #3
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    Those my friend is called a power series, they are not too terrible. Now that you know the proper name for them, looking up some information on them should not be too hard.
    To be more spefic, you will be usually told to find the radius or interval of convergence, which is done by using the ratio test.
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