logical fallacy of Functio zeta Riemanniana

$\zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}=\prod _{p{\text{ prime}}}{\frac {1}{1-p^{-s}}}$

$\zeta (s)=1+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+{\frac {1}{4^{s}}}+{\frac {1}{5^{s}}}+\ldots$

$(1- 1 / 2 s)ζ(s) = (1- 1 / 2 s)$ $+\dots$

$ζ(s) \neq Π p 1 / 1-p -s$

T.theodor 2022.9.26.