Heyyyyyy, sexy lady!

A 32 bit integer could take values upto 2^32 - 1. In practice Youtube were using a signed integer which means 1 bit was used to dictate whether the number was positive or negative, hence the value was only stored by 31 bits.

Therefore in practice only 2^31 -1 views were counted before the view count overflowed.

One Can use summation to solve This one, we have in base 2: $n_{max}=1111\dots11$ 32 times

So in base 10 it would be: $n_{max}= \displaystyle \sum_{n=0}^{31} 2^{n}$

wich is: $n_{max}=2^{31}-1$

Since the smallest number of views is $0$ and the views include all $2^{32}$ positive integers after $0$ , the maximum number of views would be $2^{32}-1$ .

Its 2^31 -1, not 2^32 -1