How do you determine the convergence or divergence of $Sigma ((-1)^(n))/(sqrtn)$ from $[1,oo)$ ?

Question

1824 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-27T11:36:18

The sum is convergent.

$sum_(k=1)^oo(-1)^k/sqrt(k)$

is an alternate series with $abs(a_k) < abs(a_(k-1))$ so it converges.

Here $a_k = 1/sqrt(k)$ .

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