Use the first six terms to predict the limit of the sequence $\alpha _ { n } = \frac { 6 n ^ { 3 } + 5 } { n + 3 }$ (assume n begins with 1).
A)0
B)94
C)2
D)135
E)the sequence diverges

Question

Quizplus · Accepted Answer

The sequence $\alpha _ { n } = \frac { 6 n ^ { 3 } + 5 } { n + 3 }$ grows without bound as $n$ increases because the numerator grows much faster than the denominator. This means the sequence diverges and does not approach a finite limit.

Use the First Six Terms to Predict the Limit of the Sequence