# If \${a_n}\$ is a Cauchy sequence of real numbers. Then, is the following statement always true?

Let $${a_n}$$ be Cauchy sequence of real numbers. Then, there exists $$alpha in (0, 1)$$ such that $$|a_{n+1} − a_n| < alpha|a_n − a_{n−1}| forall n ≥ 2$$.

I want to prove or disprove this statement. I know that latter is the definition of Contractive series.
However I’m not able to show it. Neither can I think of any contradictory example… Please give me a small hint…