McCall Search Model: Present value of lifetime income
In the version of the McCall search model I'm familiar with, once you accept an offer of wage $w$, you receive that wage $w$ in every period starting from the period of acceptance. 

Hence, from the perspective of the current period, your utility from accepting that offer is

$$ w + \beta w + \beta^2 w + \cdots =\frac{w}{1-\beta} $$

In case this equality isn't familiar, recall that the LHS is simply a geometric series.