The expression you're working with is:

\[
\lim_{{n \to \infty}} \left( 1 + \frac{1}{n} \right)^n
\]

This is a well-known limit, and it represents the definition of the mathematical constant **\( e \)** (Euler's number). The limit evaluates to:

\[
\lim_{{n \to \infty}} \left( 1 + \frac{1}{n} \right)^n = e \approx 2.71828
\]

So, the result of the limit is:

\[
e
\]

Let me know if you'd like further details on how this limit works, or any follow-up questions!

### Related Questions:
1. What is Euler's number, and where is it used in mathematics?
2. How can we prove that \(\lim_{{n \to \infty}} \left( 1 + \frac{1}{n} \right)^n = e\)?
3. Can this limit be applied in continuous compound interest calculations?
4. How does this limit relate to exponential functions and growth?
5. What other ways are there to define or calculate \( e \)?

**Tip:** Understanding limits is crucial in calculus, particularly for defining important mathematical constants like \( e \).

Explore the limit of the expression (1 + 1/n)^n as n approaches infinity, which results in Euler's number (e). This concept is crucial in calculus and exponential growth, with real-world applications like compound interest. Suitable for students in Grades 11-12.

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