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Since lim n→ infinity (.............) = ...........

Since lim n→ infinity (.............) = ...........-example-1
User DrummerB
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1 Answer

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Notice that


(4n+1)/(8n+2)=(4n+1)/(2(4n+1))=\frac12

So by the root test,


\displaystyle\lim_(n\to\infty)\sqrt[n]\left = \frac14 < 1

and so the series converges (absolutely).

User IvanJazz
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