I'm reading a proof and I don't understand one step.
1−(1−λ/n)^tn. Now, taking the limit as n→∞, P(Yn/n≤t)⟶1−e^(−λt).
How does that work out? In this case, t is time(in seconds), n is the number of Bernoulli(p) trials per second and Yn is the time until the first success.
Further, if this converges to an exponential as n -> infinity, why is this significant?