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

DrummerB asked Aug 28, 2022

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DrummerB asked Aug 28, 2022

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17 votes

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).

IvanJazz answered Sep 3, 2022

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