$4\mathrm{.}20$ Coupon collector, time to repeat

In the coupon collection problem, there are $n$ distinct coupons that we

are trying to collect. Every time we draw a coupon, we get one of the $n$

at random, with each coupon being equally likely $($the coupon we get is

replaced after each drawing$).$ Thus it is likely that we quickly see a repeat.

Define $N$ to be the r$.$v$.,$ where

$N=$ Number of coupons collected until we first get a repeat.

What is $E[N]?[$Note: You can leave your answer in the form of a sum.$]$