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Ответ

Ответ дан
igorShap

limlimits_{ntoinfty }sqrt[n]{a_n}= limlimits_{ntoinfty }arctgdfrac{1}{5^n}=limlimits_{ntoinfty }dfrac{1}{5^n}=0<1

Тогда ряд сходится по признаку Коши

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