# Average number of stickers to complete an album [duplicate]

Suppose I have a sticker album which consists of $N$ stickers. How many stickers should I buy in average to complete this album, assuming all the stickers appear with the same frequency?
More formally, let $X_1, X_2, \dots$ be independent random variables with an uniform distribution on the set $\{1, 2, \dots N\}$. Then, what is the expected value of the random variable $$Z=\min {\left\{n\in\mathbb N: \forall i\leq N,\,\,\exists m\leq n:\, X_m=i\right\}}$$
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If you have $N-k$ and just need the last $k$, the probability that a sticker will be one you need is $k/N,$ so the expected number of stickers until that happens is $N/k$. Thus the total expected number of stickers is $$N \sum_{k=1}^N \dfrac1k$$