Convergence of the infinite product $\prod_{n=1}^{\infty}\frac{1}{n^{2}+1}$

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Does this product converge? $$\prod_{n=1}^{\infty}\frac{1}{n^{2}+1}$$

any hint?

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Your hint is: It's the product of a lot of numbers each of which is between 0 and 1.