Let's think of a species which has four generations per year and which population size changes from season to season so that the population size is 100 in summer, 200 in spring, 50 in autumn and 20 in winter for example. In such case, the effective population size $N_e$ can be calculated by:
$$N_e = \frac{n}{\sum_{i=1}^n\frac{1}{N_i}}$$
where $n$ is the number of generation per year (4 in my example) and each $N_i$ correspond to the population size in one season.
My question
Can you please provide an explanation of why this formula (based on the harmonic mean) holds true to define the effective population size?