Is this : ∑ n = 1 ∞ tan ⁡ ( 1 n...

Manteo2h

Manteo2h

Answered

2022-06-27

Is this : n = 1   tan ( 1 n ! ) arctan ( n ! ) convergent sum?

Answer & Explanation

humusen6p

humusen6p

Expert

2022-06-28Added 22 answers

One has, as n ,
tan 1 n ! arctan ( n ! ) = tan 1 n ! π 2 arctan 1 n ! 2 π 1 n !
then by the comparison test the series n 1 tan 1 n ! arctan n ! is convergent.

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