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lim_(n rarr oo)e^((n)/(n))

$\lim _{n \rightarrow \infty} e^{\frac{n}{n}}$

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Simplify radical expressions involving fractions

Full solution

Q.

\lim _{n \rightarrow \infty} e^{\frac{n}{n}}

Exponential Simplification: We know that $e^{(n/n)}$ simplifies to $e^{(1)}$ because $n/n$ is $1$ for all $n$ except when $n$ is $0$ , which isn't the case here.
Constant Limit: Since $e^{(1)}$ is just $e$ , and $e$ is a constant, the limit of a constant as $n$ approaches infinity is just the constant itself.
Final Limit Calculation: So, the limit of $e^{(n/n)}$ as $n$ approaches infinity is $e$ .

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