Quotient Rule for Real Sequences/Corollary

Theorem
Let $\sequence {x_n}$ be a sequence in $\R$.

Let $\sequence {x_n}$ be convergent to the following limit:
 * $\displaystyle \lim_{n \mathop \to \infty} x_n = l$

Then:


 * $\displaystyle \lim_{n \mathop \to \infty} \frac 1 {x_n} = \frac 1 l$

provided that $l \ne 0$.

Proof
Follows directly from Quotient Rule for Real Sequences, setting
 * $\sequence {y_n} := \sequence {x_n}$

and:
 * $\sequence {x_n} := \tuple {1, 1, 1, \ldots}$