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Series converge or diverge
I have failed to determine if the following series converges or diverges, I tried using d’Alembert's ratio test and found that the limit of the ratio of two consecutive values in the general element of the series is $1$. I need to be able to tell for what values of $a$ ($a$ is real) the series converges and diverges.
$\sum_{n=1}^\infty\left((n+1)^{1/3}-(n-1)^{1/3}\right)^a$
Thanks!