My question is relatively breif: is it true that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\displaystyle \lim_{n \rightarrow \infty}(\varphi(n))=\lim_{n \rightarrow \infty}(n) \cdot \prod_{i=1}^{\infty}(1-\frac{1}{p_i})[/tex]

Where [itex]p[/itex] is prime? Pehaps [itex]\varphi(n)[/itex] is too discontinuous to take the limit of, but it would seem that as it increases to infinity the function should tend to infinity, with fewer anomalies.

If this were true,

[tex]\displaystyle \zeta(1)=\frac{1}{ \prod_{i=1}^{\infty}(1-\frac{1}{p_i})}=\frac{1}{\lim_{n \rightarrow \infty}(\frac{\varphi(n)}{n})}=\lim_{n \rightarrow \infty}(\frac{n}{\varphi(n)})[/tex]

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# Limit of the Euler totient function

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