P4550 Collecting Stamps

There are $n$ different kinds of stamps. Pipi wants to collect all kinds of stamps. The only way to collect is to buy from classmate Fanfan: each time Pipi can buy only one stamp, and which one of the $n$ kinds is obtained is equally likely, each with probability $1/n$. However, because Fanfan also likes stamps, Pipi must pay $k$ yuan for the $k$-th purchase. Now Pipi has no stamps. Pipi wants to know the expected amount of money needed to obtain all kinds of stamps.

One line, a single integer $N$ ($N \le 10000$).

Output the amount of money to pay, with two decimal places.

Translated by ChatGPT 5