Consider the series \sum_{n=1}^\infty \log(1+\frac{1}{|\sin(n)|}) Determine whether it converges absolutely or conditionally. I

Marissa English

Marissa English

Answered question

2022-01-30

Consider the series
n=1log(1+1|sin(n)|)
Determine whether it converges absolutely or conditionally.
I am trying to apply Cauchy condensation test, but I am not sure whether the given series is non-increasing or not.

Answer & Explanation

Jaiden Conrad

Jaiden Conrad

Beginner2022-01-31Added 14 answers

No, the term log(1+1|sin(n)|) is not decreasing, but since |sin(x)|1 ,it follows that
log(1+1|sin(n)|)log(1+11)

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