I have 100 papers each contains numbers like (1,2), (2,3),(3,4),..., (99,100), (100,100). I draw each paper and note down its numbers and return that paper. How any times I have to draw on average to note down all numbers from 1,2, .., 100?
Let $X_n$ be the total numbers on average drawn at $n$-time. I observed experimentally $X_{n+1}$ is around $X_n+(1-\frac{X_n}{100})2$