Question

why does the infinite sum of (-1)^n/sqrt(n) conditionally converge?

Answer 1

try the ratio test?

Answer 2

nevemind, I dont think that works

Answer 3

alternating series test

Answer 4

Conditionally means that it only absolutely converges and it diverges when the alternating series is used.

Answer 5

other way around

Answer 6

converges when alternating, but diverges when absolute

Answer 7

so if |an| converges but an does not then an conditionally converges.

Answer 8

Yes you are right

Answer 9

if it absolutely converges, that necessarily means it is not conditionally convergant

Answer 10

ok.. and i could use alternating series test on just the non absolute value part and just use p-series test on the absolute value to make it easier on myself right?

Answer 11

Group Lifesaver is correct

Answer 12

so we know that each term of the series is positive if you remove the alternating bit, and it is decreasing. If we assume the limit is 0, it satisfies the alternating series test.

Answer 13

If you prove absolute converges than you are done.

Answer 14

it is not absolutley convergant

Answer 15

conditionally convergant

Answer 16

use comparison test against absolute harmonic, it fails

Answer 17

1/n^1/2 diverges, p < 1

Answer 18

that, too.

Answer 19

the root test also fails. It converges only by alternating series test. Hence it is conditionally convergent.

Answer 20

BTW it converges to about -0.604899

Answer 21

Here is good info on AST http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

Answer 22

you need to match 2 cionditions. 1) lim(an) = 0 and 2) (an+1)/an < 1 or d(an)/dn (first derivative) is < 0 for all n > 1

Answer 23

meanwhile http://www.elitetrader.com/vb/attachment.php?s=&postid=3247424

Answer 24

applying the attention divergence test?