答：柯西积分判别法:若f(x)x>0是非负的不增函数,则级数∑[n从1到正无穷]f(n)与积分∫[1到正无穷]f(x)dx同时收敛或同时发散.记f(x)=1/(xln(x+1)),满足f(x)x>0是非负的不增函数.因为1/(nln(n+1))>1/((n+1)ln(n+1))∫[1...