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Math Help - Convergence problem

  1. #1
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    Convergence problem

    Ok, so I got a recent homework back for which I had to find the interval of convergence for the following series:

    sigma starting at j=3 and going to infinity of:
    3/(2-j) * (x+3)^j

    Now, I found the interval of convergence by doing the following:

    a_n+1/a_n = (n-2)/(n-1) * |x+3|

    If |x+3| < 1, then the series is absolutely convergent.

    -1 < x+3 < 1

    Subtracting 3 from all sides, I got
    -4 < x < -2, the interval of convergence.

    My teacher wrote on my paper that I should check the endpoints to see if they are included. How do I go about this (my teacher went over this in class, but I seem to have lost the paper I wrote it on)?
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  2. #2
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    Quote Originally Posted by clockingly View Post
    Ok, so I got a recent homework back for which I had to find the interval of convergence for the following series:

    sigma starting at j=3 and going to infinity of:
    3/(2-j) * (x+3)^j

    Now, I found the interval of convergence by doing the following:

    a_n+1/a_n = (n-2)/(n-1) * |x+3|

    If |x+3| < 1, then the series is absolutely convergent.

    -1 < x+3 < 1

    Subtracting 3 from all sides, I got
    -4 < x < -2, the interval of convergence.

    My teacher wrote on my paper that I should check the endpoints to see if they are included. How do I go about this (my teacher went over this in class, but I seem to have lost the paper I wrote it on)?
    Check the the endpoints just means to substitute that into the power series and see if it converges.
    Thus, for x=-2 , the right endpoint.
    Substitute that for x in the power series and see if it converges.
    Then do the same with x=-4.
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