#### Answer

$ \approx 2.7183$

#### Work Step by Step

We know that $a_n=1+(\dfrac{1}{n})^n$
Here, we have $a_{10}=1+(\dfrac{1}{10})^{10}=2.5937$
$a_{100}=1+(\dfrac{1}{100})^{100}=2.7048$
$a_{1000}=1+(\dfrac{1}{1000})^{1000}=2.7169$
$a_{10000}=1+(\dfrac{1}{10000})^{10000}=2.7181$
..... and so on
Hence, we can see that as the value of n increases, the value approaches to $2.7183$