Question

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (typing the series below)

Answer 1

\[\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{\sqrt[7]{n}}\]

Answer 2

And please explain why

Answer 3

for absolute, it diverges

Answer 4

Because it would be a p-series with p < 1 right??

Answer 5

you know why 1/n diverges??

Answer 6

Because its a harmonic series

Answer 7

by simple ratio comparison test.
1/sqrt(n) > 1/n ... so n diverges,

still you can take ratio comparison test to show that 1/sqrt(n) diverges

Answer 8

ahh ok

Answer 9

to show that the above series converges or diverges,

if you can show that An >= An+1 >= 0 and lim n->inf An = 0, then it converges

Answer 10

oh ok i see

Answer 11

So im kinda confused on what conditionally convergent means?? Does that mean its not absolutly convergent but it still converges??

Answer 12

if you evaluate that ... it will be + - + - + - + - ---> an alternating series, if it converges, then it is conditionally convergen

if you ignore --s and put +++ ,,, i.e taking absolute value, then if it converges, then it's called absolutely convergent.

Answer 13

ahh ok. Thanks

Answer 14

okies ... i am also learning