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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 the series diverges.
C. The Root Test says that the series converges conditionally.
D. The Root Test is inconclusive, but the series converges absolutely by another test or tests.
E. The Root Test is inconclusive, but the series diverges by another test or tests.
F. The Root Test is inconclusive, but the series converges conditionally by another test or tests.

Consider the series n1an where ann9n2n8n In this problem you must attempt to use the Root Test to decide whether the series converges Compute Llimnann Enter the class=

Respuesta :

LammettHash

Conducting the root test yields the limit

[tex]\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[/tex]

so the series converges (absolutely).

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