Let an be a sequence of positive real numbers

Problem : Let an be a sequence of positive real numbersSolution :Given a sequence of positive real numbers \[\left\{a_n\right\}_{n\geq0}\]Such that \[K=lim sup _{n\rightarrow\infty}\left|a_n\right|^\frac{1}{n}\]Then by the root test \[\sum_{n=0}^{\infty}{a_nr^n}\]Is convergent if K < 1 and not convergent if K > 1.Therefore…

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