# Probability+Calculus=Probabulus

Calculus Level pending

A bag contains $$n^2$$ black balls and $$1$$ white ball.
Now, $$n$$ balls are randomly drawn from the bag and replaced in the bag with $$3$$ more white balls, then another $$n$$ balls are drawn and replaced in the bag with $$5$$ more white balls, then $$7$$ balls and so on till $$2n-1$$ white balls.
If $$P_n$$ is the probability that all balls drawn are $$BLACK$$, then find $\lim_{n \rightarrow \infty}P_n$

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