I4.2 Consider fractions of the form $\frac{n}{n+1}$, where $n$ is a positive integer. If 1 is subtracted from both the numerator and the denominator, and the resultant fraction remains positive and is strictly less than $\frac{\alpha}{7}$, determine, $\beta$, the number of these fractions.
$$
\begin{array}{l}
01 \\
1<n<7
\end{array}
$$

Possible $n=2,3,4,5,6$
$$
\beta=5
$$