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**Kat-M** Let $\displaystyle f$ be a funtion from $\displaystyle R^+$ to $\displaystyle R$ such that $\displaystyle f$ is of bounded variation on $\displaystyle [0,n]$ where $\displaystyle n \in Z^+$. Let $\displaystyle V_f (0,n)$ be the total variation of $\displaystyle f$ on $\displaystyle [0,n]$. In addition, $\displaystyle f$ satisfies $\displaystyle \mid f(n)-f(0)\mid \leq M_n$ and $\displaystyle \sum_{n=1}^\infty M_n \leq \infty$.

Determine whether or not $\displaystyle lim_{n\rightarrow\infty} V_f (0,n)$ exists.