Does #a_n=x^n/n^x # converge for any x?

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Does #a_n=x^n/n^x # converge for any x?

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Answer 1 · 2018-05-27T12:11:01

#"No"#

Explanation:

#"If "x = -1", we have "a_n = n*(-1)^n" and this alternates"#
#"between "-oo" and "+oo" for "n->oo, " depending on the"#
#"fact if n is odd or even."#
#"If "x < -1", the situation gets even worse."#
#"There is only convergence for "x > -1.#

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Does #a_n=x^n/n^x # converge for any x?

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