Consider all even natural numbers. Every 4th number has a power of 4 (or $2^2$)
Every 8th number has a power of 8 (or $2^3$)
Every 16th number has a power of 16 (or $2^4$)
What is the average number of power of 2 in any random even number?
Since every 2nd number has a power of 2,and every 4th number is a power of 4 and so on
$\left(2 \times \dfrac{1}{2}\right) + \left(4 \times \dfrac{1}{4}\right) + \left(8 \times \dfrac{1}{8}\right) + \ldots$
This goes all the way to Infinity and hence the answer is $\infty$. Is this correct?