There are in?nitely many boxes.

There are in?nitely many boxes. The ?rst box has one white ball and one black ball. The second box has one white ball and two black balls. The ith box has one white ball and i black balls. You will start at the ?rst box.Randomly pick one ball from the current box. If the ball is white, the game ends. If the ball is black, you progress to the next box and repeat this action.What is the probability that the game ends after you take exactly n balls?

 

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