I was wondering how to determine whether this series converges: <munderover> &#x2211;<!-- ∑

veneciasp 2022-07-01 Answered
I was wondering how to determine whether this series converges:
k = 1 ( k + 1 ) ! k k ?
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Answers (1)

Jordan Mcpherson
Answered 2022-07-02 Author has 16 answers
Noting
lim k k k ( k + 1 ) k = lim k ( 1 + 1 k ) k = e 1
you have
lim k | ( k + 2 ) ! ( k + 1 ) k + 1 ( k + 1 ) ! k k | = e 1 < 1
which implies that your series converges.

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