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Esmeralda Lane

Esmeralda Lane

Answered question

2022-07-14

Determine the convergence of n = 2 sin ( n π + 1 ln n )

Answer & Explanation

Alec Blake

Alec Blake

Beginner2022-07-15Added 11 answers

( 1 ) n sin ( 1 ln ( n ) ) converges by Leibniz Test .
But sin ( 1 ln ( n ) ) is divergent by comparing with 1 ln ( n )
That is
lim n sin ( 1 ln ( n ) ) 1 ln ( n ) = 1
And 1 ln ( n ) diverges by Cauchy Condensation test.(Or just by simple comparison with 1 n as mentioned in the comments.)

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