Pregunta
Find the limit of the following sequence or determine that the sequence diverges.
Select the correct choice below and fill in any answer boxes to complete the choice.
A. The limit of the sequence is
. (Type an exact answer.)
B. The sequence diverges.
Select the correct choice below and fill in any answer boxes to complete the choice.
A. The limit of the sequence is
B. The sequence diverges.
Ask by Turnbull Guerrero. in the United States
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The limit of the sequence is 0.
Solución
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
- step1: Rewrite the expression:
- step2: Calculate:
- step3: Rewrite the expression:
- step4: Calculate:
- step5: Rewrite the expression:
- step6: Rewrite the expression:
- step7: Rewrite the expression:
- step8: Calculate:
- step9: Calculate:
The limit of the sequenceas approaches infinity is .
So, the correct choice is:
A. The limit of the sequence is .
A. The limit of the sequence is
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To find the limit of the sequence
, we can analyze the behavior as
approaches infinity.
We can factor out
from the denominator:
As
approaches infinity,
approaches 0 and
also approaches 0. Thus, the limit becomes:
Therefore, the limit of the sequence is:
A. The limit of the sequence is
.
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