Question

Test to see if the series \[\sum_{n=1}^{\infty}{\frac{(-1)^{n+1}}{^4\sqrt{n}}}\]is absolutely convergent, conditionally convergent, or divergent.

Answer 1

use the divergence test

Answer 2

...

Answer 3

\[\lim_{n\to\infty}\frac{2^n}{\sqrt[4]{n}}=\infty\]

Answer 4

oops that's the wrong series, the first one is actually correct. sorry

Answer 5

sorry I feel sleepy I've been doing homework for the last 6 hours.

Answer 6

the first one converges conditionally

Answer 7

yeah since 1/root(n,4) does not converge, but it passes the alternating series test.

thanks.

Answer 8

with the absolute value, it's a p series wiht p < 1 so it's divergent.