20．（2023•山东模拟）已知函数$f(x)=\frac{{3^x}-1}{{3^x}+1}$，数列$\{a_{n}\}$满足$a_{1}=1$，$a_{n+3}=a_{n}(n\in N_{+})$，$f(a_{1})+f(a_{2}+a_{3})=0$，则$\sum\limits_{i=1}^{2023}{a_i}=($　　$)$