Real numbers/geq 1/Higher roots/Monotonic/Convergence/Exercise

Let ${}b\geq 1$ be a real number. We consider the real sequence

${}x_{n}:=b^{\frac {1}{n}}={\sqrt[{n}]{b}}\,$

(with ${}n\in \mathbb {N} _{+}$).

1. Show that the sequence is decreasing.
2. Show that all members of the sequence are ${}\geq 1$.
3. Show that the sequence converges to ${}1$.

Create a solution