Number Theory

    

Conditions for Convergence of the Sequence 1/(��^��|sin��|^��)

Authors: Yudai Sakuma

It is known that if the sequence 1/(��^��|sin��|^��) converges then ��(��)≤1+��/�� , but the convergence of this sequence has not been solved. In this study, the conditions for convergence of 1/(��^��|sin��|^��) were clarified by focusing on �� such that the value of |sin��| becomes explosively small. As a result, it was confirmed that ��(��)<1+��/�� is a sufficient condition for convergence of 1/(��^��|sin��|^��) . This is the same result as in the previous study, but because the method of proof is different, we succeeded in identifying a range of values for lim��→∞1/(��^��|sin��|^��) when ��(��)=1+��/�� .

Comments: 4 Pages.

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Submission history

[v1] 2024-07-09 02:37:35

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