NL-NWO 1962 Problem 2

The $n^{th}$ term of a sequence is $t_n$ . For $n \ge 1$ , $t_n$ is given by the relation: $$t_n= n^3+\frac12 n^2+ \frac13 n + \frac14$$ The $n^{th}$ term of a second sequence $T_n$ , where $T_n$ represents the smallest integer greater than $t_n$ . Calculate: $$(T_1+T_2+...+T_{1014}) -(t_1+t_2+...+t_{1014})$$