Prove that [tex]\prod_{j=1}^{\infty}\left(1-\frac{1}{f(j)}\right)>0[/tex] for all [tex]f:\mathbb{N}^{+}\to\mathbb{R}^{+}[/tex] which satisfy [tex]f(1)>1[/tex] and [tex]f(m+n)>f(m)[/tex], where [tex]m,n\in\mathbb{N}^{+}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I found the problem "Prove that [tex]\prod_{j=1}^{\infty}\left(1-\frac{1}{2^{j}}\right)>0[/tex]" and felt the need to make a generalization of it. So, here it is!

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# Generalization of infinite product problem

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