How do I solve this question?

4. For :1: any real number dene the fractional part of :r, denoted {1:} to be the difference between :1: and the largest integer less than or equal to I. Show that there is an increasing sequence of natural numbers 351, jg, . . . , 3}, . . . so that for every natural number I, the inequality Him/5} {j:+1\\/}| S 2! is satised. Hint: The BalzamJ-Weierstrass theorem might help