The limit of the sequence $a _ { n } = \frac { \ln n } { n ^ { 2 } }$ is

A)0
B)1
C) $- \frac { 1 } { e }$
D) $1 - \frac { 1 } { e }$
E)$\infty$

Question

The limit of the sequence $a _ { n } = \frac { \ln n } { n ^ { 2 } }$ is

A)0
B)1
C) $- \frac { 1 } { e }$
D) $1 - \frac { 1 } { e }$
E)$\infty$

Quizplus · Accepted Answer

The limit of the sequence $a_n = \frac{\ln n}{n^2}$ as $n$ approaches infinity can be found using L'Hôpital's Rule or by recognizing that the numerator grows logarithmically while the denominator grows quadratically. As $n$ becomes very large, the denominator increases much faster than the numerator, causing the fraction to approach 0.

The Limit of the Sequence an=ln⁡nn2a _ { n } = \frac { \ln n } { n ^ { 2 } }an​=n2lnn​

The Limit of the Sequence $a _ { n } = \frac { \ln n } { n ^ { 2 } }$