Question 81
For a positive integer $k$, let $a_k = \lfloor \frac{2^k}{k} \rfloor$. Prove that the sequence $(a_k)$ contains infinitely many odd numbers.
($\lfloor x \rfloor$ denotes the largest integer not greater than $x$.)
($\lfloor x \rfloor$ denotes the largest integer not greater than $x$.)