Show that in the sequence: x, 2x, 3x, .... (n-1)x (x can be any real number) there is at least one number which is within 1/n of an integer.

Show that in the sequence: x, 2x, 3x, .... (n-1)x (x can be any real number) there is at least one number which is within 1/n of an integer.

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