14. For Example 2j show that the variance of the number of coupons needed to amass a full set is equal to

$$

\sum_{j=1}^{N-1} \frac{jN}{(N-j)^2}

$$

When N is large, this can be shown to be approximately equal (in the sense that their ratio approaches 1 as N → ∞) to N²(π²/6).