Problem

Let

S_n = 1+2+3+\dots+n

and

P_n = \frac{S_2}{S_3} \cdot \frac{S_3}{S_4} \cdot \frac{S_4}{S_5} \cdots \frac{S_n}{S_{n+1}}

where

n \in N

(

n \ge 2

). Find

\lim_{n \to \infty} P_n