how would you find the value of :
$$ \left(1-\frac{1}{2^2}\right) \left(1-\frac{1}{3^2}\right) \left(1-\frac{1}{4^2}\right) \ldots \left(1-\frac{1}{2017^2}\right)$$
Tried looking for some kind of pattern here but in vain .
thanks in advance
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2Use a telescope. – Donald Splutterwit Sep 23 '20 at 12:29
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2Does this answer your question? For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$. See also Find the value of x – Sil Sep 23 '20 at 12:31
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$(1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{4^2}).......(1-\frac{1}{2017^2})=$
$(1-\frac{1}{2})(1+\frac{1}{2})(1-\frac{1}{3})(1+\frac{1}{3}) .......(1-\frac{1}{2017})(1+\frac{1}{2017})=\frac{1009}{2017}$
Lion Heart
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