Let and , where…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

S_k = 1 + 2 + 3 + \dots + k

and

Q_n = \frac{S_2}{S_2 - 1} \cdot \frac{S_3}{S_3 - 1} \cdot \frac{S_4}{S_4 - 1} \dots \frac{S_n}{S_n - 1}

, where

k, n \in N

\lim_{n \to \infty} Q_n =

(a)

\frac{1}{3}

(b) 1 (c) 3 (d) 0