MathDB
Long sequences

Source: AHSME 1991 problem 25

October 30, 2011
AMC

Problem Statement

If Tn=1+2+3++nT_{n} = 1 + 2 + 3 + \ldots + n and P_{n} = \frac{T_{2}}{T_{2} - 1} \cdot \frac{T_{3}}{T_{3} - 1} \cdot \frac{T_{4}}{T_{4} - 1} \cdot\,\, \cdots \,\,\cdot \frac{T_{n}}{T_{n} - 1} \text{for }n = 2,3,4,\ldots, then P1991P_{1991} is closest to which of the following numbers?
<spanclass=latexbold>(A)</span> 2.0<spanclass=latexbold>(B)</span> 2.3<spanclass=latexbold>(C)</span> 2.6<spanclass=latexbold>(D)</span> 2.9<spanclass=latexbold>(E)</span> 3.2 <span class='latex-bold'>(A)</span>\ 2.0\qquad<span class='latex-bold'>(B)</span>\ 2.3\qquad<span class='latex-bold'>(C)</span>\ 2.6\qquad<span class='latex-bold'>(D)</span>\ 2.9\qquad<span class='latex-bold'>(E)</span>\ 3.2