Each of 2010 boxes in a line contains a single red marble,

and for 1<(equal) k <(equal)2010,

the box in the kth position also contains k white marbles. Isabella begins at the first box and successively draws a single marble at random from each box, in order. She stops when she first draws a red marble. Let P(n) be the probability that Isabella stops after drawing exactly n marbles. What is the smallest value of n for

which P(n) < 1/2010 ?

The answer is 45.

I first tried to figure out the probability for her to pick white marbles.

the first box 1/2

second box 2/3

third box 3/4

fourth box 4/5

I think I'm stuck....