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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.

 Jan 2, 2022
 #1
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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.  

 Jan 2, 2022

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