Question 66
Determine the remainder when
$$
2^{\frac{1 \cdot 2}{2}} + 2^{\frac{2 \cdot 3}{2}} + \cdots + 2^{\frac{2011 \cdot 2012}{2}}
$$
is divided by $7$.
$$
2^{\frac{1 \cdot 2}{2}} + 2^{\frac{2 \cdot 3}{2}} + \cdots + 2^{\frac{2011 \cdot 2012}{2}}
$$
is divided by $7$.