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Use the limit comparison test to determine whether ∑n=7[infinity]an=∑n=7[infinity]9n3−6n2+76+3n4 converges or diverges. (a) Choose a series ∑n=7[infinity]bn with terms of the form bn=1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n≥7, limn→[infinity]anbn=limn→[infinity] (b) Evaluate the limit in the previous part. Enter [infinity] as infinity and −[infinity] as -infinity. If the limit does not exist, enter DNE. limn→[infinity]anbn =

Respuesta :

Answer:

It does not converge.

Step-by-step explanation:

Since

[tex]6n^2 \leq 9n^3[/tex]

and

[tex]0 \leq 9n^3 - 6n^2[/tex]

Adding  7 on both sides of the inequalty we get

[tex]7 \leq 9n^3 - 6n^2 +7[/tex]

and     we know that the sum [tex]\sum_{n=0}^{\infty} 7[/tex]    diverges.  Therfore by the comparison test  

[tex]\sum_{n=0}^{\infty} 9n^3 - 6n^2 +7[/tex]

Does not converge.

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