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Math Help - [SOLVED] Power Series(Radius and interval of convergence)

  1. #1
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    [SOLVED] Power Series(Radius and interval of convergence)

    hey there.. i hope u guys can help me..
    the question is...
    Determine the interval and radius of convergence of the power series below..
    \sum\limits_{k=0}^\inftyk!(x-3)^k

    i've already find the radius, r = 0
    then..
    c - r < x < c + r
    3 - 0 < x < 3 + 0
    hence, x = 3

    when x = 3..
    \sum\limits_{k=0}^\inftyk!(3-3)^k = 0

    so.. the interval of convergence is 0..
    am i do it right?
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  2. #2
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    Quote Originally Posted by nameck View Post
    hey there.. i hope u guys can help me..
    the question is...
    Determine the interval and radius of convergence of the power series below..
    \sum\limits_{k=0}^\inftyk!(x-3)^k

    i've already find the radius, r = 0
    then..
    c - r < x < c + r
    3 - 0 < x < 3 + 0
    hence, x = 3

    when x = 3..
    \sum\limits_{k=0}^\inftyk!(3-3)^k = 0

    so.. the interval of convergence is 0..
    am i do it right?

    Well, the interval of convergence could be put as \{3\} = [3,3] , but I guess that depends on the teacher's taste. At any rate, 0 is not an interval but a single number.

    Tonio
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