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[tex]\sum[/tex](-1)

^{n-1}*[tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex])

is it enough to say that

lim {n->inf} [tex]\frac{n-1}{n+1}[/tex]*(1/[tex]\sqrt[n]{n}[/tex]) is not 0 ???

i know for regular series this would be okay but what about series with alternating signs??

how else can i tbe proven??