Question 37
Evaluate the sum
$$
\left\lfloor \frac{1}{13} \right\rfloor + \left\lfloor \frac{3}{13} \right\rfloor + \left\lfloor \frac{3^2}{13} \right\rfloor + \dots + \left\lfloor \frac{3^{101}}{13} \right\rfloor.
$$
Here $[\dots]$ denotes the integer part of a number.
$$
\left\lfloor \frac{1}{13} \right\rfloor + \left\lfloor \frac{3}{13} \right\rfloor + \left\lfloor \frac{3^2}{13} \right\rfloor + \dots + \left\lfloor \frac{3^{101}}{13} \right\rfloor.
$$
Here $[\dots]$ denotes the integer part of a number.