Math2400
  • Math2400
Does the series converge absolutely, converge conditionally, or diverge?
Mathematics
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Math2400
  • Math2400
Does the series converge absolutely, converge conditionally, or diverge?
Mathematics
katieb
  • katieb
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Math2400
  • Math2400
\[\sum_{n=1}^{\infty} \frac{ (-1)^{n+1} }{ \sqrt{n} } \]
Math2400
  • Math2400
this is an alternating series one. So bn=1/sq(n)
Math2400
  • Math2400
I know it converges

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Math2400
  • Math2400
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Math2400
  • Math2400
using p-series it's divergent......so the answer is 'conditionally convergent' ???
Zarkon
  • Zarkon
conditionally convergent is correct
anonymous
  • 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.
Math2400
  • Math2400
thanks :)

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