Im trying to determine whether or not the following series converges: <munderover> &#x2211;<

dikcijom2k

dikcijom2k

Answered question

2022-07-14

Im trying to determine whether or not the following series converges:
n = 1 + 1 n log ( n ! )

Answer & Explanation

amanhantmk

amanhantmk

Beginner2022-07-15Added 17 answers

Since n ! = 1 2 3... n 2 n 1 , we can use the comparison test with
n = 2 1 n log ( 2 n 1 ) = 1 log 2 n = 2 1 n ( n 1 )
the latter of which clearly converges, since 1 n 2 converges.

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