Am I correctly determining the convergence or divergence of these series: &#x2211;<!-- ∑ -->

Keenan Santos

Keenan Santos

Answered question

2022-07-08

Am I correctly determining the convergence or divergence of these series:
1 n ( ln ( n ) ) 5 / 4 )

Answer & Explanation

behk0

behk0

Beginner2022-07-09Added 14 answers

Your reasoning is not correct. Hint: Note that 1 x ( ln x ) 5 / 4 = ( 4 ( ln x ) 1 / 4 ) and use the Cauchy-Maclaurin integral test.
aangenaamyj

aangenaamyj

Beginner2022-07-10Added 5 answers

Use Cauchy's Condensation test:
2 n 2 n log 5 / 4 ( 2 n ) = 1 log 5 / 4 2 1 n 5 / 4
and since the series with general term from the right converges (why?), also ours does.

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