Arithmetic mean greater than or equal to geometric means is a well known ineqaility.
Use that to show that
$$\left(1 + \frac{1}{n+1}\right)^{n+1} \gt \left(1 + \frac{1}{n}\right)^{n}$$
[Solution]
Use that to show that
$$\left(1 + \frac{1}{n+1}\right)^{n+1} \gt \left(1 + \frac{1}{n}\right)^{n}$$
[Solution]
