lim(n->∞)(lnn)^2/n=0f(x)=(lnx)²/xf'(x)=[2lnx-(lnx)²]/x² =lnx(2-lnx)/x²当x＞e²时,f'(x)<0即此时un>u(n+1)所以由莱布尼兹判别法,得该级数收敛....