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? asked in Science & MathematicsMathematics · 9 years ago

Find the radius of convergence, R, and the interval of convergence, I, of the series?

The sum from 1 to infinity of ((x-8)^n)/(n^n)

1 Answer

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  • kb
    Lv 7
    9 years ago
    Favorite Answer

    Due to the nth powers, this is best done with the Root Test.

    r = lim(n→∞) |(x - 8)^n / n^n|^(1/n)

    ..= |x - 8| * lim(n→∞) 1/n

    ..= |x - 8| * 0

    ..= 0.

    Since r = 0 < 1 for all x, this series converges for all x (with infinite radius).

    I hope this helps!

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