Barry has a standard die containing the numbers 1-6 on its faces.
He rolls the die continuously, keeping track of the sum of the numbers he has rolled so far, starting from 0 . Let E_{n} be the expected number of time he needs to until his recorded sum is at least n.
It turns out that there exist positive reals a, b such that
\lim _{n \rightarrow \infty} E_{n}-(a n+b)=0
Find (a, b).