# Limit of Constant Sequence

A sequence $\{x_n\}_{n=1}^{\infty}$ is said to converge to c iff for any $\epsilon > 0$, $\exists K\in \mathbb{N}$ so that $\forall n > K, |x_n - x_K| < \epsilon$. In this case we say the $x_n \rightarrow c$
In your case your function is constant and is c for every n, so $|x_n-x_0|=|c-c|=|0|=0 < \epsilon$ for all $\epsilon >0$ this proves your sequence converges to c by choosing K=0 in the definition.