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Let f(n) = n^2/(n^2 - n + 1).

 

Find the largest integer n such that f(2) * f(3) * f(4) * ... * f(n) < 1.98.

 Jun 14, 2021
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\begin{eqnarray*}
    f(2) &=& 1.33333 \\
    f(2)\cdot f(3) &=& 1.71429 \\
    f(2)\cdot f(3) \cdot f(4) &=& 2.10989
\end{eqnarray*}
This table shows that the largest such $n$ is 3.

 Jun 14, 2021

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