I'm studying for an exam and came across this question. I feel like it's much simpler than I am making it out to be, but I'm not sure.
Suppose we have a corpus in which Zipf’s Law holds. If the most frequent term occurs one million times, and the next most frequent term occurs 250,000 times, how often should we expect to see the third most frequent term? And the fourth most frequent term?
Wikipedia has the formula $$f\left(k,s,N\right)=\frac{\frac{1}{k^{s}}}{\sum\limits_{n=1}^{N}\frac{1}{n^{s}}},$$ We but in this problem, $N$ (the number of terms) and $s$ (the value of the exponent characterizing the distribution) aren't given. Only $k$ (the rank) is given and the frequencies of each rank. I know that Zipf's Law says that the frequency of a term is inversely proportional to the term's rank, but I don't know what that constant factor would be in $f_{t}=c\cdot\frac{1}{k}$.