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I have to determine whether the given series diverges or converges. [tex]\sum[/tex] cos(n*pi)/(n^(3/4)) where n= 1 and goes to infinity.

I tried a couple numbers for n and got:

-1 + 1/(2)^(3/4) - 1/(3)^(3/4)

Hence I came up with the series: [tex]\sum[/tex]((-1)^n)/(n)^(3/4) where n=1 and goes to infinity.

I guess my main question is that now that I have that new representation of the series, why can't I just take the absolute value of the series and say that it is a p series with p< 1 and therefore diverges.

My book took the limit of the series and got 0 and said it converged. Why can't you use the p-series test???

Thank you,