Find the average number of children a couple has.


THis is :


1(1/2) + 2(1/2)^2+ ... n(1/2)^n +...


(rearrange terms) = 1/2 + 1/4 + ...


+ 1/4 +1/8 +....


+...


= 2


now multiply by the number of couples.


All that was used here was the geometric formula and some rearrangement of terms.