Question 44
Determine the remainder when
$$
\sum_{i=0}^{2015}\left\lfloor\frac{2^{i}}{25}\right\rfloor
$$
is divided by $100$, where $\lfloor x\rfloor$ denotes the largest integer not greater than $x$.
$$
\sum_{i=0}^{2015}\left\lfloor\frac{2^{i}}{25}\right\rfloor
$$
is divided by $100$, where $\lfloor x\rfloor$ denotes the largest integer not greater than $x$.