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1991 AMC 12 Question 25

AMC12 · 1991 AMC 12

Question 25

If $T_n=1+2+3+\cdots+n$ and $$
\begin{aligned} P_n&=\frac{T_2}{T_2-1} \cdot\frac{T_3}{T_3-1}\\ &\quad\cdot\frac{T_4}{T_4-1} \cdots\frac{T_n}{T_n-1} \end{aligned}
$$ for $n=2,$ $3,$ $4,$ $\ldots,$ then $P_{1991}$ is closest to which of the following numbers?
  1. $2.0$
  2. $2.3$
  3. $2.6$
  4. $2.9$
  5. $3.2$