<s>[INST] How does one evaluate the multiplication $f(2)\cdot f(3)\cdot f(4)\cdots f(15)$ by formulating? Suppose 
$$f : \mathbb{Z}^+ \rightarrow \mathbb{R}$$
$$f(x) = 1-\dfrac{1}{x^2}$$
How does one evaluate the multiplication $\prod_{i=2}^{15} f(i)=f(2)\cdot f(3)\cdot f(4)\cdots f(15)$? 
Here I have to see the trick that directly yields the calculation. 
How come that we write this using $\Pi$ (product) notation? I'll be glad to hear your dear thoughts. 
 [/INST] Hint: $f(x) =  \frac{x^2-1}{x^2} =  \frac{(x-1)(x+1)}{x^2}$

and take product of $f(2),f(3),...,f(n)$
Look:
$$
\frac{(1)(3)}{2^2} \cdot \frac{(2)(4)}{3^2} \cdot \frac{(3)(5)}{4^2} \cdot ... \frac{(n-3)(n-1)}{(n-2)^2} \cdot \frac{(n-2)n}{(n-1)^2} \cdot \frac{(n-1)(n+1)}{n^2} = \frac{1}{2} \cdot \frac{n+1}{n} $$
 and take this for your task
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