5
QuizMultiple Choice

Limits as They Relate to Sequences and Series — Quiz

Question 5 • Precalculus

Which statement describes the sequence defined by A sub n is equal to the fraction with numerator n squared minus 16 and denominator n cubed plus 4 ?

Answer
A
The sequence diverges.
B
The sequence converges to 0 .
C
The sequence converges to 1 .
D
The sequence converges to infinity .

Explanation

As n gets larger, the highest-power terms determine the fraction’s behavior: (n² − 16)/(n³ + 4) behaves like n²/n³ = 1/n. Since 1/n approaches 0 as n increases, the sequence converges to 0, so the correct statement is “The sequence converges to 0.”

AI-written and checked against the verified answer.

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