用根值法Un=[n/(3n-1)]^(2n-1)lim n→∞ Un^(1/n)=lim [n/(3n-1)]^(2-1/n)=lim [n/(3n-1)]²*[n/(3n-1)]^(-1/n)=lim [1/(3 -1/n)]²* 1=1/3²=1/9＜1所以该级数收敛。
