…meanwhile, on a fictional math Olympiad event…

(calculators are not allowed)

1. …

2. …

3. Assume that all N-sided die have an equal probability of giving a number from 1 to N. Start by rolling a 100-sided dice. Then you roll a N-sided dice with N as the previous roll result. That continues until you rolled 1.

   Find the average amount of rolls you need to get 1.