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(sum T_i -sum t_i), t_n= n^3+ 1/2 n^2+1/3 n + 1/4

Source: Netherlands - Dutch NMO 1962 p2

January 31, 2023
Sequencefloor function

Problem Statement

The nthn^{th} term of a sequence is tnt_n. For n≥1n \ge 1, tnt_n is given by the relation: tn=n3+12n2+13n+14t_n= n^3+\frac12 n^2+ \frac13 n + \frac14 The nthn^{th} term of a second sequence TnT_n, where TnT_n represents the smallest integer greater than tnt_n. Calculate: (T1+T2+...+T1014)−(t1+t2+...+t1014)(T_1+T_2+...+T_{1014}) -(t_1+t_2+...+t_{1014})
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