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Determine all values of p for which the series: n = 2 ( 1 ) n 1 2 n ( l n ( n )

Determine all values of p for which the series: n=2(1)n12n(ln(n))p is convergent, expressing the answer as interval notation. (see photo if what I typed looks off)

Upon a couple attempts, I keep getting (-infinity, 0) as my answer. I am not sure if I am applying the alternate series test correctly.

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