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

veneciasp

veneciasp

Answered question

2022-07-01

I was wondering how to determine whether this series converges:
k = 1 ( k + 1 ) ! k k ?

Answer & Explanation

Jordan Mcpherson

Jordan Mcpherson

Beginner2022-07-02Added 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
that suggests your series converges.

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