Corollary 2 [Contractive Sequence Theorem] If $\left({x}_{n}\right)$ is a sequence, for which there is a number $C<1$ such that $|{x}_{n+2}-{x}_{n+1}|\le C\cdot |{x}_{n+1}-{x}_{n}|$, then $\left({x}_{n}\right)$ converges;