The question asks: "Let
. Find the largest integer n so that <span>f(2) · f(3) · f(4) · ... · f(n-1) · f(n) < 1.98"
The answer is n = 98</span>Explanation:
First thing, consider that the function can be written as:
Now, let's expand the product, substituting the function with its equation for the requested values:
As you can see, the intermediate terms cancel out with each other, leaving us with:
This is a simple inequality that can be easily solved:
200n < 198(n + 1)
200n < 198n + 198
2n < 198
n < 99
Hence, the greatest integer n < 99 (extremity excluded) is
98.