Question 5
In this paper, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$. For examples, $\lfloor5\rfloor=5$, $\lfloor2.8\rfloor=2$, and $\lfloor-2.3\rfloor=-3$.
It is given that $S=\dfrac1{1\times2}+\dfrac1{2\times3}+\dfrac1{3\times4}+\cdots+\dfrac1{2014\times2015}$. Find the value of $\lfloor4030\times S\rfloor$.
It is given that $S=\dfrac1{1\times2}+\dfrac1{2\times3}+\dfrac1{3\times4}+\cdots+\dfrac1{2014\times2015}$. Find the value of $\lfloor4030\times S\rfloor$.