Question

How do you determine the convergence or divergence of `Sigma ((-1)^nsqrtn)/root3n` from `[1,oo)`?

Answer 1

The series is not convergent as it does not satisfy Cauchy's necessary condition.

Explanation:

If we write the general terms of the series as:

`a_n = sqrt(n)/root(3)n = n^(1/2)/n^(1/3) = n^(1/2-1/3) = n^(1/6)`

we can see that:

`lim_(n->oo) a_n = oo`

so the series cannot converge.