3}\right)^a$ is convergent

Asked Dec 10 '12 at 21:15

Active Dec 10 '12 at 21:20

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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!

edited Apr 13 '17 at 12:19

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asked Dec 10 '12 at 21:15

Itakmar

Please use $\LaTeX$. – glebovg Dec 10 '12 at 21:18
What you wrote was unambiguous, but $\LaTeX$ does make the mathematics easier to read; for future reference you can find $\LaTeX$ help here. – Brian M. Scott Dec 10 '12 at 21:23

How do to determine if $\sum_{n=1}^\infty\left((n+1)^{1/3}-(n-1)^{1/3}\right)^a$ is convergent

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