I want to determine the convergence of the series to do so, consider that ( n

dikcijom2k 2022-07-01 Answered
I want to determine the convergence of the series to do so, consider that
( n + 1 ) n 3 n n ! ( n + 1 ) n 3 n
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Answers (1)

Tristin Case
Answered 2022-07-02 Author has 15 answers
So,
n = 1 ( n + 1 ) n 3 n
diverges, and, yes, you always have
( n + 1 ) n 3 n n ! ( n + 1 ) n 3 n .
It doesn't follow from this that
n = 1 ( n + 1 ) n 3 n n !
diverges.
You can use the quotient test:
lim n ( n + 2 ) n + 1 3 n + 1 ( n + 1 ) ! ( n + 1 ) n 3 n n ! = lim n ( n + 2 ) n + 1 3 ( n + 1 ) n + 1 = lim n 1 3 ( 1 + 1 n + 1 ) n + 1 = e 3 < 1 , and therefore your series converges.
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