Probability of Both

Robert picks a number $N$ randomly from the set of positive integers such that the probability that $n$ is selected is $2^{-n}$ for each positive integer $n$ . He then puts $N$ identical slips of paper numbered $1$ through $N$ into a hat and gives the hat to Charlotte. Charlotte does not know the value of $N$ , but she draws one of the slips uniformly at random and discovers that it is the number $2$ . What is the expected value of N given Charlotte’s information?