Mathematics: Consider the series ∑n=1∞an where an=(n+9)n(2n+8)n In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L=limn→∞|an|−−−√n Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L= Which of the following statements is true? A. The Root Test says that the series converges absolutely. B. The Root Test says that

Consider the series ∑n=1∞an where an=(n+9)n(2n+8)n

meme6229

15.08.2021

Conducting the root test yields the limit

$\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\frac{(n+9)^n}{(2n+8)^n}\right|} = \lim_{n\to\infty}\frac{n+9}{2n+8} = \frac12 < 1$

so the series converges (absolutely).

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tylerkrobinson7853

26.01.2020

1.5 times

Step-by-step explanation:

is the answer

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