用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]

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用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]

用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]
用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]

用根值判别法判定下列级数敛散性n*tan[π/2^(n+1)]
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