Find the limit of the sequence if it converges; otherwise indicate divergence.
-$$a _ { n } = \left( 1 + \frac { 2 } { n } \right) ^ { n }$$
A) 1
B) $e ^ { 2 }$
C) e
D) Diverges

Question

Quizplus · Accepted Answer

The sequence $\left( 1 + \frac { 2 } { n } \right) ^ { n }$ is a classic example of an expression that approaches $e^{k}$ as $n$ approaches infinity, where $k$ is the constant in the fraction. In this case, $k = 2$, so the limit is $e^{2}$.

Find the Limit of the Sequence If It Converges; Otherwise an=(1+2n)na _ { n } = \left( 1 + \frac { 2 } { n } \right) ^ { n }an​=(1+n2​)n

Find the Limit of the Sequence If It Converges; Otherwise $a _ { n } = \left( 1 + \frac { 2 } { n } \right) ^ { n }$