Question

Let $$f(x) = \frac{x^2}{x^2 - 1}.$$Find the largest integer $n$ so that $f(2) \cdot f(3) \cdot f(4) \cdots f(n-1) \cdot f(n) < 1.98.$

Answer 1

f(x) = x^2/(x^2-1)
It might help to visit

https://math.stackexchange.com/questions/312381/proving-prodk2-1-k2-n1-2n-by-induction

to see that

n
Π (k^2-1)/k^2 = (n+1)/(2n)
k=2

so, you want n such that

2n/(n+1) < 1.98