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

Question

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

Quizplus · Accepted Answer

As $n$ increases, the numerator $n + 2$ grows linearly, while the denominator $n^3 + 2$ grows cubically. This means the fraction $\frac{n + 2}{n^3 + 2}$ gets smaller and smaller, approaching 0 as $n$ approaches infinity.

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