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.
+20 n=3
calculating a few terms, we have f(2)=4/3
f(3)=9/7
f(4)=16/13
f(5)=25/21
We see that each term becomes larger than the last (easily proved and intuitive)
Thus, we know that the product will keep on increasing as n increases.
letting n=3, we have the product equal to 12/7, or about 1.714
n=4, the product is about equal to 2.110.
From this, we know the largest value is n=3.
