If the integer part of x is denoted by [tex][x][/tex] fractional part of x is denoted by [LaTeX ERROR: Convert failed] , then you can see the following:

[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

You can formulate it as a statement: f(n) gets arbitrarily close to an integer as n goes to infinity. Then maybe you can prove it. This is better than what you state, because we not only see that the function is close to an integer for big n, but it's getting closer and closer to an integer.

[LaTeX ERROR: Convert failed]