## Math2400 one year ago Does the series converge absolutely, converge conditionally, or diverge?

1. Math2400

$\sum_{n=1}^{\infty} \frac{ (-1)^{n+1} }{ \sqrt{n} }$

2. Math2400

this is an alternating series one. So bn=1/sq(n)

3. Math2400

I know it converges

4. Math2400

|dw:1433702724096:dw|

5. Math2400

using p-series it's divergent......so the answer is 'conditionally convergent' ???

6. Zarkon

conditionally convergent is correct

7. anonymous

Yes, conditionally convergent. You can show the absolute value of your a_n diverges by p-series. Then you refer to the altrnating series test and as you showed, its convergent under those conditions so yes, conditionally convergent.

8. Math2400

thanks :)