用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]
问题描述：
用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]
答
因为
lim（n趋向于+∞）{ntan[π/2^(n+1)]}^(1/n)
=lim [nπ/2^(n+1)}^(1/n)
=1/2lim (nπ/2)^(1/n)
=1/2