Question 33
Evaluate the sum
$$\left\lfloor\frac11\right\rfloor+\left\lfloor\frac12\right\rfloor+\left\lfloor\frac22\right\rfloor+\left\lfloor\frac13\right\rfloor+\left\lfloor\frac23\right\rfloor+\left\lfloor\frac33\right\rfloor$$
$$+\left\lfloor\frac14\right\rfloor+\left\lfloor\frac24\right\rfloor+\left\lfloor\frac34\right\rfloor+\left\lfloor\frac44\right\rfloor+\left\lfloor\frac15\right\rfloor+\cdots$$
through the $2013$th term.
$$\left\lfloor\frac11\right\rfloor+\left\lfloor\frac12\right\rfloor+\left\lfloor\frac22\right\rfloor+\left\lfloor\frac13\right\rfloor+\left\lfloor\frac23\right\rfloor+\left\lfloor\frac33\right\rfloor$$
$$+\left\lfloor\frac14\right\rfloor+\left\lfloor\frac24\right\rfloor+\left\lfloor\frac34\right\rfloor+\left\lfloor\frac44\right\rfloor+\left\lfloor\frac15\right\rfloor+\cdots$$
through the $2013$th term.