Chapter 11 - Section 11.1 - Sequences - Exercise Set - Page 640: 57

multiple answers; see details

Given that $ a_n=\left( 1+\dfrac{1}{n} \right)^n $, then, \begin{array}{l} a_1=\left( 1+\dfrac{1}{1} \right)^1 =2 ,\\\\ a_2=\left( 1+\dfrac{1}{2} \right)^2 = 2.25 ,\\\\ a_3=\left( 1+\dfrac{1}{3} \right)^3 \approx 2.3704 ,\\\\ a_4=\left( 1+\dfrac{1}{4} \right)^4 \approx 2.4414 ,\\\\ a_5=\left( 1+\dfrac{1}{5} \right)^5 \approx 2.4883 .\end{array}