Use the first six terms to predict the limit of the sequence $a _ { n } = \frac { 5 n ^ { 3 } } { n ^ { 3 } + 3 }$ (assume $n$ begins with 1 ).
A) 4
B) 5
C) $\frac { 23 } { 6 }$
D) $\frac { 32 } { 5 }$
E) the sequence diverges

Question

Quizplus · Accepted Answer

As $n$ approaches infinity, the $3$ in the denominator becomes negligible compared to $n^3$, making the sequence approach $\frac{5n^3}{n^3} = 5$.

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