please explain how this formula was derived, by the geometric mean formula?

being unemployed the third month times 1, and so on. Thus we get the duration of unemployment as 1 1 1+(1x)-1+(1x)'-1+(1x)'-1+...== l(lx) x _ 1 _ 1 Af+v As +v Au+s where we have used the fact that f a: s/(lu + s). The duration of unemployment depends on three factors: 0 A higher rate of unemployment means that there are more workers competing for available jobs and less chance to nd a job, which leads to a longer duration of unemployment. o A high rate of separations (people leaving jobs) means that there are more job openings, so the duration of unemployment decreases. o A high rate of exit from the labour force also reduces the duration of unem- ployment, as more workers and their unemployment spell by dropping out of the labour force