There are n urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i = 1, 2, 3, \ldots, n$ and W denotes the event of getting a white ball. If $P(u_i) \propto i$, where $i = 1, 2, 3, \ldots, n$, then $\lim_{n \to \infty} P(W)$ is equal to